{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 从观察到的数据中发现因果关系\n",
    "# 导入包\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import dowhy\n",
    "from dowhy import CausalModel\n",
    "import dowhy.datasets, dowhy.plotter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Treatment    Outcome        w0\n",
      "0   9.038605  18.664537  3.483516\n",
      "1   9.398023  19.126242  3.470221\n",
      "2   8.507360  16.267672  2.071781\n",
      "3   2.333234   4.458025 -3.990660\n",
      "4   9.870889  19.884446  3.865623\n"
     ]
    }
   ],
   "source": [
    "# 创建数据集。它由以下两种模型之一产生：\n",
    "# 模型1：干预确实会导致结果。模型2：干预不会导致结果。\n",
    "# 所有观察到的相关性都是由于共同变量造成的\n",
    "rvar = 1 if np.random.uniform() >0.5 else 0\n",
    "data_dict = dowhy.datasets.xy_dataset(10000, effect=rvar, sd_error=0.2)\n",
    "df = data_dict['df']\n",
    "print(df[[\"Treatment\", \"Outcome\", \"w0\"]].head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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BS2eL4NAh80JswQJ95ySiAV1d5ctcfXXw9dCMQZ/KMwxzu1zdKiRtpTbZrDlpUacHHkjXhRNRGNascVauAjLw5WPQp/IymWBy61dI2kqtslkza5+InvP19bG1T6Tbpz/trFwFbLCTj0GfSrNa+TqXpdTVmeet9DX5XmUyQE2NvvPdey/X7xPptH+/s3IV2FPJoE+lBdHKT1u3fr5168xeDp1mz9Z7PqK0MgznZSuwp5JBn0pbu1Z/8ok0duvb5Sfw0THOv2ULx/aJdHDaIKnQpGIM+lSYYQDTpwM7dgBVGt8mlbJVbph0TfBrbfV/DqK0e/jh8mWqqir2O4xBnwprbQWefx7Yvt1/S3/MmGTk1Q+SjteFM/mJ/Nuxo3yZUaOCr0dAGPTpSIYBLF2q73zjx+s7V1IZhv/tOfv70z1Xgsgvp3uKVPB32pCoK0Ax1NqqZxx/8mTg97/3f540yGT0vOZOU4cS0ZHmzStfpqGhonss2dKnwXS28l99Vc95ks4wzFz6Omb0b9/u/xxEadTe7qycrhwbEWHQp8F0tPInTzYnulRgispI6GrlA8DevcB3v6vnXERp8olPOCvHoE+JsnKl/3P84Q9mEONOcM7oXrc/f76+cxGlxc6dzspV2K56+Rj0aTCl/B1fXT2QbS7tSXicCmLdPlv7RM45zbUPVPR4PsCgTxZr61wnO0uV0tc30Grt6WFr3wsd6/bnz+frTuTUnDnly1RX+28UxQCDPpkyGeA3v9GfHpatfW/srf+GBm/n+Mxn9NaJKGkMAzjrLGDXrvJlq6oScSHNoE8Dm+oEcRWb9pS7fhkGsGePt2OffZYb8RCVkskA69c7K9vbm4gGDNfpE3DNNcDBg3rONWwY0N2t51xkfsn09Xk//tJLuXSSqBCrsePGs88GU5cQsaWfdoYBrFrl/fiqKjOhhdUVzYCv17p1/o7fuhWYNi0R3ZJEWrndQVTEnPdU4Rj00+6aa/wd39/P7vsg6ZjU9+KLieiWJNLGSojlJj+GUon4rmPQT7vVq70fO2wYN9EJgzWpz0/wv/NOtvaJLF4SYg0blojvOgb9NFuzxnsmOI7dh8/PF05PD1v7RBa3CbFEEvN9x6CfZk7WphaTkA9ARXGaG7yYu+5ia58IGOg9c7IctrZWX5rsGGDQT7POTm/H+d0ClryZO9ff8QcPsrVP5NakSVHXQCsG/TS74AL3xzQ1sZUfla1b/Z/Dz0oNoqRx8l2WsCWvDPpp5WWpXnV1IiayVKzu7oGlkV53+uroMH9aaZfZ3U9pduBA+TJTpgRfjxAx6KfV5z7n/pgEjWtVvP5+cwtjtw4dMrP0ZTLAb3/L7n5Kr8WLy5cZPTpxDR0G/TQyDODpp90f9/nP668Leee12/GTnxxYo8wNkSitFiwoX2bcuODrETIG/TTyGrw5HhwvX/iCt+MMw2zxA9wQidLJMJyVa24Oth4RYNBPo1/9yttx48frrQf54ydFrxX0uf0xpZHThk8CGzqOg76YThGRq0TkNhH5HxE5KCJKRMrOhhCRe3Nly93+yd9/iUpas8bbcWPGJG5sq+JZa439Ymuf0sZpwyeBDR03u+ydAOAPQVWEQnLZZd6OS+CbPxEMw5zJ7yf4c/tjShOnDZ/a2kQ2dLx273cAeBTAbzwc+1sAR5e4/ZvHOlEx1vKsjRuBvXvdH89WfnxlMkBNjbdjRcz3BvdPoDRpaYm6BpFyE/TfA9AC4H1KqfFKqUsBPOPhOfuUUvtK3FzsdUiOWMuzLrnE2/Fs5ceX2xzidkoBX/yi3voQxZlhAF1dzspefXWwdYmI4+59pdReAI8FWBcKgmEAd99tLs968033xzMhT7zZ/zZVVe67+R9/XG99iOLs+uudl03okBdn7yddJgP0+ug8SVg2qkTr7weuu85dd39/P/CMlw47ogpjGMDDDzsr29SU2MZOZEFfRKpFpDqq508FeyvfiwS/8RPJMMzld24v8j796WDqQxQn11zjrNzkyYn+3osi6E8Rka0AegD0isg7IvKoiHjY/YVK8tPKZ8CvPJmMtwu8PXvM1LxESeVmr5GPfCTYukQsiqA/CsD7c88tAI6FOUFwlYg8LCJ1EdQpmdau9RYEEphvOhX8TOq79FK9dSGKEzdj+StXBlePGAgz6L8NYDGAcwBMBFAL4H0ArsDA+v/LANxb6iQicq2IbBCRDTt27Aissokwc6a34/bvZ4a2SmQl62lqcn/s1q38m1MyuRnLB4AJE4KrSwyEFvSVUq1KqQVKqWeVUn9SSvUopd5WSv0cwEcAPJcrOltE/qrEeX6qlGpWSjWPHTs2lLpXrLVrvR3X08MMbZXMa6Y+/s0pidy08g0j8b2csZi9r5TqAmCfZfHZqOqSKJMmeTuuvz+xy1VSxe3Wu173ZCCKK7et/NbW4OoSE7EI+gCglPpfANZeoR76J+kwwwDOOsv9ZhGTJ5stRGZoSwa3wzt9fcHUgygqbnuvErjBTr7YBP2c7bmf9ZHWotJlMsD69e6PO/ts/XWh6Lgd3tm6lWv2KVnc7kSZguyjcQv643I/OyOtRSWz1mp7wS79ZJk5Exg61N0xn/gEJ/RRcmSzwPvf77z86tXB1SUmYhP0ReRUmEv5AIB9y15lMt66admlnzxel/DdcIP+uhBF5a23nJdNwWTWUIK+iIwrlX1PRI4CcKftnx4MvlYJ5DUjm5clXhR/1ix+pYCGBufHPfQQk/VQMrS3AwcOOC+fgt5OxxvuAICIfBjASNs/jR94SKbnFc8qpQ7m7n8GwJdE5AEAzwL4I4D9AEbDXLffCuD/5MouVUp5XGuWcl4ysjU0sIVPR/roR4E33gDGjStblCiWDAOYnh+Wijj5ZGDLlmDrExOugj6AHwMoNNtrKID8GRMnAnjD9vtJABaVOf89AP7eZZ3I8vTT7rtzq7n9QSpUuezUO3gQuPZaYPduYNkyBn+qPDfcYL6Pndi6Ndi6xIjboO/VowCqAZwFYDKAMTBn6HcB+BPMxDx3KaX+O6T6JI9hANu2uT9u3z5z4ha/1JNtwgTgvffcHWOlI81kgNtu018noqC4XZ+fot1ERXnJ3BUTzc3NasOGDVFXIx5mzXL3JreImNux8ks9HU49Fdi82d0xdXXAa6/xwpAqx0UXAY8/7qxsdTVw6FCw9dFMRF5QSjV7OTY2s/fJB7dXtXZKpWLyCuV46cZkWmaqJIbhPOADwIc+FFxdYohBPwnc5JbOxy1006W7Gxg2zN0xfX3mqhCu36dK4HbJacqSkjHoVzo/rXwG/HR67TX3x/T2srVPlWHFCnflU9bTGdZEPgqKly9iEfdL+yg5vLxnDh1K3ZcjVSDDcLeCaejQ1DV82NKvdF62z62t1V8Pqhxu85FbUpCilCpcJgMMcdGWTeEmUwz6lW7aNHflq6vNcV1Kr2zWXWpSSwq2HaUKt26du4ykKVqqZ2HQr2SGATzoMmNxCt/kVICXLv4UbDtKFe6JJ5yXHTYsdV37AIN+ZfOyuU4K3+RUgJcu/lGj9NeDSKfZs52XTWmPJ4N+pTIM4O67o64FVapsFhg92t0xNTXB1IVIB8MAfvtbZ2VFgq1LjDHoV6pMxnleaQt30yO7CRPcld+8mbvvUXy5WZ8/dGhw9Yg5Bv1K9cwzzsuKmJn32LVPdk884X7DJTfdp0RhcZuv5LOfDa4uMcegX6nc7JngZgkLpYeXOSGvvhpMXYj8uOEGd9+J1mZSKcSgX4kMA3jlFeflUzx+RSV4mczX18d0vBQvhgEsX+7uGLdDWwnCoF+J3K6XdpOhitIjmzVbR5MnuzvObW5zoiC5+T5saEj9UCeDfiVyu16aE/ioFLc77z30EFv7FB+PPea8bGdncPWoEAz6lcYwgK4u5+VTflVLDnjZgIetfYoDwwB273Ze/rrrgqtLhWDQrzSZjPOkElX885IDXrLztbXprweRW263FeemUQz6FcUwgDvucF7ezWxWSi8vmzb19HDNPkXPzSx8EW4aBQb9ytLaam5x6hS3zyUnZs70lqyEa/YpSm630RXx1quVMAz6lcIwgAcecF7ebYpVSq9167yt8HCzbJRIt9ZWd72Z/f3s3geDfuW4/np3b/AUr0Mll6yle26X7ynFWfwUDS87jM6bx0nNYNCvHG6WpRx9NN/c5M20ae7KX3ttMPUgKqW11X02SbbyATDoV4b2dqC313n5vXuDqwslm9scEG7LE+ng9n1XW8uGUA6DfiWYM8dd+WHDgqkHJZ/bYaH+fnebPxH5ZRjuGzZuJkAnHIN+3LnNsw8Ar78eTF0o+Z54wv0xl1+uvx5ExWQy7ieeTpkSTF0qEIN+3LnNsw9wWQp55+W9s2sXJ/RROAwDuO8+5+WZa/8IDPpx52ULSE5YIa+87LwH8EKTwpHJuEtDzlz7R2DQjzO3eaUBczyfV7XklX353jHHOD/uV78Krk5EgPl9eM897o5hrv0jMOjHWSbjLqvevHnO8/ITlXPggPOy3L6Zgub2+xBgr2cBDPpx5jYnOt/gpJOI87JvvMFZ/BQcq5XvNu0uez2PwKAfZx/+sPOynKxCunV3u1v+ee65nNBHwfDSyufeIwUx6MeVYQAPPxx1LSjturuB6mpnZfv7gQULgq0PpdPatRxC0oRBP44MA2hqcpdrn9ucUlDcrHG+/3629km/mTPdlZ83L5h6JACDfhxlMsD27e6OueKKYOpClM0CVQ6/KtjaJ928zNp/9tlg6pIADPpxYxjA3Xe7P27rVv11IbIMGeK87L33sueJ9PEynn/22cHUJQEY9OPGS4pJpbhUj4Lldkcz9jyRDlYjyO13IlcyFcWgHydWN5absXxurkNhcJu7/A9/4Ng++ZfJuNthlGl3y3LRZ0eBy2TctahmzwaWLQuuPkSWbNa8wDx40PkxmQxw223B1YmSb+1ad137TleaBKwt24GvP7oJ+3vM73MBcOX0ifh2S/Qb/7ClHyfr1rm7qn3sseDqQpTPTbIepcxeK7b2yY+ZM4GaGufljzsuuLo41JbtwFeWbzwc8AFAAVi6fhsWtm2KrmI5DPpx4naGqpsvYSK/urvNYO70fXfoEDfiIe+s4U6nDSGRWEzgW/LkFvT1Fx6iXbp+W8i1ORKDfpzMmeO87JgxnLxH0TjxRGflens5oYq8czvcqVQs3m9vdcb7e5lBPy4MA3jlFeflx48Pri5Epbz2mvOynFBFXrkd7hw9OvL3W1u2Ay6mYUeCQT8uWludl21qivzNTSnmZsUIU0mTF4bhfmXShAnB1MWhtmwHvrysPdI6OMGgHweGATz4oLOyF13EgE/RcjOs9NnPBlcPSq5MBli/3nn56urIvxdvWbk59q18gEE/HtyMXa1cyRnRFC3DcF720CHglFP4niVnDAOYNg24/XZ3x7nNI6FZW7YDu7pcDEVEiEE/Dtatc1fezVAAkW6ZDDB0qPPyL7/MfPzkTCYDvPii++NWr9ZfFxeWPLkl0ud3g0E/DrJZYNYs5+VXrQquLhWsLduBGYufwYmtqzBj8TNoy3YEckzqrVvnPi0qd9+jcrzuOwJEvjS0I+Yz9u0cZ+QTEQHwIQAftd1OAzAUwEGllKNZFyJyHICvALgYwEQAXQA2A7gXwL1KuclBmxCGASxf7rw8Z+4P0pbtwKIVm9HZPdC91tHZjfkPbwQAtExtHFR2yZNb8FZnN46pq8H+nkPo7VOHj1nwyKYjjqE89rFTp2v2rd333OaioPTIZNxlfLSLaKme9X1SScRpjBWRSQBeL/Kwo6AvIs0AVgE4tkiRXwJoUUo5+ss3NzerDRs2OCkab+eeC/zqV87KzpvH1KY2bdkOzF++Eb1FkmEIcHhyjf1+KdUi+N7s0w8HfvuFwvH1dZh//gd5UQCYF6vHH++8fFUV0NEBjBsXXJ2oMhmGmf/BS9CP6DuxLduBm5a1w+X+f3hj8YW+n1tEXlBKNXs51mvu/Q4A/w1gDIC/dHKAiIwBsAJmwH8PwA0AngZwDIB/BPAPAD4J4N8BXOuxXpXJacAHUrNPtNNAu2jF5qIBHxgc5J12IfUphRuXtePGZe2oEsB+evYG2LjtUmVrn4pxu7GOXUSt/AWPvOQ64MeBm6D/Hij2+nEAACAASURBVIAWAM8rpd4GABFZBIdBH0ArgPcB6Afw10opaz3G2wC+JCJVAK4D8Hci8u9KqeiTFIfhF79wXnbo0FikmQxaW7YDCx7ZhO5ec0VDR2f34SBcX1eDRRdPRsvURrRlOwZ16Qeh0PVEd2/f4fpYvQeNaewBcDsBFQAefZRBn460bp27jXUAc0e9nTuDqY8D3b3uQ351DFKnOw76Sqm9ADzt8CIiNQD+LvfrY7aAb3dzrkwNgC8C+JKX56o4n/+887I9PbFIMxkEe8u+SgR9RYadOrt7DwfcOLBqmcoegGwWmDoVaHfxt2DqaCokmwWuusqc8OlUTHbUc+OzZ0abQAgIb/b+X8LsxgeAgim6lFI7AFh91xeHUanItbc769KqqjLzSid0n2irZd/R2Q0FFA34cWf1AEz91lPpWQWQzbp7T/b0AC+9FFx9qHK53TU0wh31vH6+07S17jTb/edLlLMem5CbA5Bsl13mrFyFBkGnljy55XBXfhLs6urF/Ic3pifwz53rrvyFF5rDVFzCR3Z79zovG+FQp9VIcWvGSaMCqI17XifyuXVy7mc/gDdLlLOvDvgggHcDq1EcON24xO1YV4WJ+65UXvT2KdyycjMAJH/m/9at7sr/+c/mLP5MhitRyPSLX7j7notwqNNLI+UDx47Ag9ecFVCN3AmrpW+12ncppQ6VKLfddn90gPWJnptUpgm2sG1TReSr9mJXlzn/wBq2sMb9E9cD4GWcXilzQh9b+wS4m9tUXR3pUKfbRDwCYM1N5wRSFy/CaumPyP08UKac/dU8KqC6xIObVLpvv52Ytc3WhL1KymClU3dvH5Y8uSV5rf2mJncT+gAzLz9b+/SLX7hbrjd0aEV9J8atURNWS99ap1Du/29fz1CwrIhcKyIbRGTDjh07tFQudIYBLF3qvHzEKSa9yk9xu7Bt0+EJe2nW0dmdvJS/2az7rVB7e820q2ztp9tVV7kr39cX2Xfiwjb3Y/mN9XUB1MS7sIL+vtzPcv97+7fG/kIFlFI/VUo1K6Wax44dq6VyoWttdTd+VYHL9PJn5Hd0dmPp+m2JmrDnR0dnN76yPGGT/bx08/f0VOxFLWmwZo37fRwiGs9vy3Zg6fptro+bf/4HA6iNd2EFfWtCXr2IlBpSsEfx9wKsT7RWrHBetqmpIpfp3bJyMwN8GX39Zua/Sa2rMPmbv0zGBUBtrbvy/f2pyTJJeQwDOP98d8cMHWqm3Q35O7Et24Eve8gNMuOkUbEbygtrTP+V3M9qmJvsFJu2fqLtfmXtYuCUYQCdnc7LV2DAr6S9peNif0/fEUmH7NkHK4aXjGOTJ+uvB8VbezvwkY+4X44cUSv/q//5kuux+RknjYrNjH27sIL+C7b7Z6J40D8z93ObUiqZy/XcTOBragquHpoUypG/aMXmqKuVCJ3dvbjpIfMioGICf3c3UF8P7N7t/Jjly4F/+7eKmZhFGsyZY07kdGvy5NAbQlfesQ4HD7lbNh3XgA+E173/GwDWt8DlhQrkkvFY2RZWhlGpSLjJOnXffcHVQ4NC4/Y3PdQeeD78NOlXOLzev2K4HdtXytyIh9KhvR145ZXy5fJVVYWekKct24HntrrP7x/XgA+EFPSVUr0A7sz92iIiHy1QbBGAoTBn7f80jHpFws0X4qxZwdVDg0JJKkpseEceVdxQSZ+HuRyPPKK/HhRPc+Z4O66/P/Su/ST2Wrrq3heRDwMYafun8QMPyfS84lmllH1z5MUAroC5094qEbG21h2Jga11AeBOpVRyk3O76dJym+ksZEnMpBdXk1pXYXhNFbp7++Of2W/KFPdr9vfsqai11+SBYZgpmL208gFg9OjQu/a99Fo2DK8JoCb6uB3T/zEGuuDthgLI32fzRABvWL8opd4VkYsBrAJwLIAHC5znlzAvAJLLzVK9KdFvzlBMpc00r6kCRtTWVPTQQ1duK8/Y7+hnfTG7ndR3ww3AsmX660PxkMn4C9oTot+hzombL4r3xNSwxvQBAEqpDQBOA/BdmDP6uwHshDnm/wUAF+T1DiSL09bP6NGx3lGvLduBmx5qj12mqWJqqgVLZjWh/ebzcOucpqLJMiTvZ5xZmf1izW2ynuXLmagnqQzDTLvs1pgxke0w6rVhE8sLcRtXLX2l1Dl+n1Ap9Q6A+blbujjdjSxmV7T2GfrH1FVWa3l4TRX+5dLTDn8QW6Y2Hr5faOWB9djCtk342fPbYj1HIfaZDbu7zQvdqVOdlVfK7N3atInd/EmTyXjbOGxUdDvTff1R99n3KoGoCt62tbm5WW3YsCHqajhjGMDxxzsvG5MvPWuGfhwT7TQMr8GB3j509x75ZdIwvAY3X6R3jXtbtgNfeWgj+mLymREAP5jTFO+WxamnAptdToaaN4/5+JPEMID3vx84UG7rlQImTwZ+/3v9dSqhLduBr/7nS66X6QFmbo32m88LoFaDicgLSqlmL8eGtU6f3KQajdEmJItWxCOznojZEGwsMImtVItdJ+uccbkIUgC+9shL8Q76Xiaj3nMP8I1vxObCl3zKZLyt6ABCn8zclu3A/Ic3orfP/YV9TZVg0cXxHs8HGPTDYRjAXXc5Lx+TXPtt2Y5Iu/KdZqSzd9kHzXqeW1ZuPmIpXV1NNYbVVIW6xK6rtx+TWlcBCKZ3w7fubnMrVDddu9aGKjG58CWf1q1zt4ueJYIU5Eue3OIp4FdS9kx274dh3jzg9tudlY2gO6uYplueCj3oz50+Ed9uie+qBbtCPQxAtD0BNdWCJZefHq8vnzFjgPdcbqVRVwe89hpb+0lgGOY8JTet/aoqoKMj9L+/dQHthgB4ffGF+itT6jnZvR9zTz/tvGzIGacKWdi2CT9//k+hjl3XVAmWzIpZsCqjVA/Dkie3RDLRrrdPYcmTW+L1Ok6Y4D7os7WfHK2t7rv3+/vNLI1eZvx75HW2fqU1m9nSD8NJJ5mtFici3lVvYdsmT9tH+lFonD5pwp4QGbvuRrf5+AFgxAjg1VfZ2q9kXlr5loYGYKf7FLhenfKN1QUnBZfTWF+H51o/HkCNimNLP+6cBvyIZ+173S/ajyg+MFGwgu+Xl4WT36Czuxfzl28c9NyR8jJze/9+JuypdF5a+ZaqUNPIeAr4NVVyeFivUoT7qlJpbmb4a9aW7TgcJMKUplS+LVMb8YM5TaF96Hr7VXwS+HjZchcAHnqICXsqlWEADxZKvOpQiPlKzv3+rz0dV2lDkgCDfrxEOGt/0YrN6I0gE83xRbLjJVXL1EZ8f04T6uvCyc/d0dmNGYufiT5tstud9+xuuEFfPSg8N9zgvpU/eXIkGfj+uH2/62NujXuOjCIY9INkGMD0/H2Iiohgn2jA3Ct6UuuqwGfpV8GcWW5XV1NdcV1jOrRMbUT7zefhjcUX4tY5Taj22gp2yMrVH3ngb2rydhxb+5XFMICzzjLTKrsVwUTmhW3uM++JxGTYzAMG/SBlMsDzzzsrG8GOelfesc7TXtFuzZ0+Ea8tvhBLLj8djfV1EJhj+d+5dErFfnB0aZnaiO/NPv2ICyLdunv7ot8m9IknvHfzs7VfOTIZYP16b8dG0Nv5s+fdz2O68syJAdQkHJy9HxQ3OccBszsrZF7WpDolQPy3gI2RtmxHwYQ/ukU6q3/ePDNJVU+P+2NrarwdR+EyDODEE4GDHvZNiyD98rnf/7Xrrv0PHDsCa246J5gKOcTZ+3HkdHMdwHyzJ8jwmir8IfOpqKtRUaw1/0FeiAHmrP7ItuVdt8574O7tNbv4uXwv3jIZbwEfCL2Vf+Y/r8E7e929H6uAyAO+X+zeD0J7u7tNRkJ+s7dlO/CBrwUTXKoE+JdLTwvk3GlQbNtfnSLbljeb9T6uD7CLP+4MA7j7bm/HioQ6p+nKO9a5DvhA5SXiKYRBPwhuWvlXXRXqm91amudhSWpZjfV1+P7sypzRGhfzz/8g6mqqA3+ejs5unNi6KvyZ/dmsOZTlZWyfE/riLZPxlmN/3jxv2+561Jbt8DyXKQmrjdi9r5thAH/4g/Pyq4Ltzs13y0q9S/PqaqrwHdt+9eRPqQ19dFMYmNlvf+5QfPjD7rfcBZiaN87WrvUWvEPu6bxlpbcJrUlZbcSWvm6ZjDnpyKnx44Ori01btgNTv/WU1kBy65wm/G/mUwz4mrVMbUT2m+fh1pDW80fS3e91tcqdd5rLwdjij59p09wfE/J6/IVtmzx/ByZltRFb+rq5mawkAqxeHWx9YL7RH1y/Tet4VMPwmkR8AOLMvqGPtaNfUJv4hL45UHc3cOqp7lv7PT3mcrAzzgBefJET++LEy7r8EPlJMz68piox33ds6euWzQLXXeesbE1NoKl327IdOOUbq7FUc8CvrhLcfNFkjWekclqmNuK51o/jjcUXhjLZL3Buh8EKHc+JffFgJSHzk3UxQG3ZDjTd8hRuXNbu6fikTU5m0A/CE084K9fTE9h4Vlu2Azcta/e0iUQ536vAfNNJEtRkPy+ZyTxzOwxWyPLl7OaPg2uucZ6EzK6hQX9d8lgTl71mHE3i5GQG/SD8+c/lyzQ1BTqeteCRlxDEfNjG+rpEfQAqUcvURnzn0iloGK53vH/p+m3hBX4/a/YtSrG1H7X2du+TkauDX6Wy5MktviYuP9f68cR93zHo69beXn6TiYaGQCevtGU7AmnhJ2X2ahJYk/1mnDRK63mXrt8WzhI+a+meUua+E16xtR8+wzBz5L/9NnDJJd7PE8IkZj+7eAabGDs6DPq6OfkQBJxyN4iZ2PV1NYmZvZokD15zFuZOn6j1C+rGZe1ouuWp8Nbvz5zp/VilzF4zBv7wZDLAb39r9rJs8zYxDkAos/aP8bH65crplZtfvxQGfZ0Mw9mHIMAJLwvbNmmdid1YX4db5zSh/ebzGPBj6tstU/C65gl+VrreUAL/unX+jn/nHaC1VU9dqDTDAO65x1yP/9BD3s8zbJi+OhXRlu3A3oOHPB07d/pEfLtliuYaxQODvk7XXx/ZU7dlOzD5m7/0vCSlkFvnNCVyTCup/HRlFtLd24cvL2sPPvBns/7Hd5cuZWs/DJmMv+x5NTVmBr4QZvrfsnIz+jyO5yc14AMM+nq1tTkrd/XVep8224H5D2/E/p4ycwlcmDt9IoN9hQkiRagCcFMYgb++3t/xfX1s7QfNauX7mYDZ2xt4Bj5rqbLXJDyJWBJbAoO+ToccdiVpftN//dFN6O3TN0+gvq4m0Ve6SRXUUr5+AF975CXt5x1kwgT/52BrP1h+W/kAUFsb+CRmP0uVBUj8ZGUGfV3WrHFWTuOb3kqtq7OFX1dTjUUXM/FOJbKW8jXW12mfedzV2x9sa9+aze80sVUhbO0Hy+8yy5oa7b2c+Rat2OxrqfKVKejhZNDXZdasUJ+uLduBBY94zyNdSGN9HWfoVzgrc9/riy/Unrd/0QpvG5W44ndS34oVeupBg7W3A3/8o79zhNC17zUJD2Cm2k1DDyeDvg6GAeze7ayspivdJU9uQXevvhb+G4sv5KS9hFl08WTUVOlr83d29wY/tv/EE/5mdu/dyy7+IMyZA+zf7+8ckyeHurmOW0lKtVsKg74ObroUn31Wy1PqnKk9N6HrUdOuZWojlsw6HdVe9q4vwuu2pI75HTc+dMjcjIeBX5/2duCVV/yf5+yz/Z+jhCvv8N5LNOOkUalp8DDo67BypfOymt74uqbtJXk9KpmB/3uzT9c2xr+rK+DWvo70vIYBLFigpz5ktvJ1CLBrf2HbJjy3dafn4x+85iyNtYk3Bn0d3HxJ+Xjjt2U7MGPxM5jU6jHXtc2Mk0bhjcUXMuCnQMvURlypMWtfoEl7rAl9TU3+znPvvcDTTw+kiyV3rJ3zTjvNfyvfMALdZ2Rh2yZf+UmSvkQvH4O+Dk7GuiZP9vXGtybu6ci2VzukKlVXtmQmG/nBnCYtXf3dvX24cVk7Zix+JvjgP3q093NccomZLjbA7asTK5Mxd87b5HMDpqFDA339/Qb8Kkn+Er18DPp+GYazcq++6utpdE3cq64S/L/L0jFhhQazuvp1Te7r6OwOPlWvn/X7+/eb8wPuvputfTcMA7jrLj3nCnD7cAB40EfArxYkbttcJxj0/XI6ic/nrH1dE/e+N+v01L3JaYA1uU/Xcr7u3r5ANng6TEeK3p4etvbdyGT8z6sAAt8+HPA3t2nrdy5M5Xchg75fTifx+bjaXdi2ScvEvWqRVL7JabCWqY1ov/k8NAzXE/g7OruDbe37TdHL1r5zOlv5q1frOU8R537/156PHV6T3tCX3v+5DoYB7NpVvpyIp6tdK4e0rk10PnumhlSnlBidGhM7zV++MbjAryNF74EDZgvWvhc8HUlXK986V0CuvGMd/rjde96AtKzJL4RB3w+nb+q33nJ9amvintcc0vm4NI/y6dygp7dfYUFQ+fmzWf+z+QEzR4a1Fzy7+wtbu1bfuTTlJMnXlu3wtTzv1jnpG8e3Y9D3yjCAO+90VtbDF4yuiXtcmkfF6N6gp7u3HwvbfM72LiabNVfA+PH+9w/sBX/PPWztF+r1OOUUfecPIBnPwrZNuHFZu+fjG4bXpDrgAwz63mUyZi5pJzyM5+tYmgekK+kEuWPfoEeXB9dvC66bf+ZMf8evXGluygOYmfvS3tov1Ouhc+8CzbP2/S7PA4CbL+JmYgz6XjndGMTj7FUdi6rSlnSC3LM26Hlj8YVa0jErBJiqV0fXs3Wh3ttrTu4766z0tPjtLXvDGOj1+PGPgeXLzWQ8fsbzN240v++sm+ZZ+34D/geOHZH6Vj7AoO9dwBtH+J2tX1dTnbqkE+TPt1umaAn8u7p6feVBL2rmTKBK41fWgQPA+vXpafHbW/b5exzMnWsm4/Hjiiv8HV9EW7YDTbc85fs8a246x39lEoBBP0ijRrk+RMcbfMTQam6RS558u2UKPnDsCN/neW7rTv3j+2vX+tuMp5g0jO/bW/Z3323e7K16HTP2t271f448bdkOzF++0deWuTQYg75Xt99evozLlKdt2Q7ctKzd1xt8xkmjsPlbn2TAJ8/W3HSOlhb/z57Xs9T0sJkzzbSuuqVhfD+TGZjPcOAAcPCgvnNfdZXZnd+tb+dPy4JHXkJvv/8sJRzqHMCg74VhAPPmlS/ncn3xohWb4acdM+OkUZy4R1p8u2UK3lh8oa9Wv4bv6sF07MBXSG/vka39JK3nt1r5Ticeu7XK/wZghbRlO7QtWeZQ5wAGfbcMAzj1VGdlXYz7t2U7fHdhMeCTbmtuOsdX4D/lG6txYusqPZvz6NiEp5iDB4EpU4CRI4GXXkrWen57Kz8I48cHctqvP6pneIjL9AYbEnUFKk5rK7DTYWKIt98Gxo0rWaQt24FbVm7GLo3Z0Yh0WnPTOZ63c7ZaatbmPAD8fwFPmAC8956/c+Tr7wfefde8P2sWsG3bwHr+b3yj7Oc41tatC66V39SkdVJzW7YDS57cgrc6u7WkHq+rqeYyvTyhtfRFZJKIKAe3fWHVyTXDAB580Hn5Mq2EtmwH5j+8UUvA55gVxZ22zXmsFr9SejL15XvllYEx776+ym/tP/EEMGyY3nPOm6d9WZ59+3AdAb+xvo4Tmgtg974bra3uusnKJKe4ZeVm9Pb5f3tzeR4FTdfmPLp2izwsmwVqa/WeEzADGmDOIaj02f35y/N0CGC7XF1ZSGuqBbfOacJzrR9nwC8gqqB/AYCji9yOi6hOpblt5Tu4CtbRwq8W4dUsBe7miyajptp/yqghQXzjuFwl41pfn3nBH8eJfaUmHFqPrV2rbwJkQ0Ng2+XqyELaWF+HJZdz+/BSogr63UqpfUVu3rdOCpKbyTANDcHWJaeuphrfm803OAWvZWojllx+uu9hpN5+6E/c090dTDe/pacHePxx4De/Ac44I16Bv9SEw9ZWM+Bv2QLU6Ompwe7dgfz/daRurhKwde8Au/edcpp2F3CcNWyoz5YTW/gUJitlr1/Pbd2pPz+/rp34CjnjDGDfPrOFaxhmMI0De8Id+xCEYQDTpgH332/+fuiQvol8/f2BzHHQMdfjijP955ZIAwZ9p7JZ5ylAy6zPb8t2YOq3nkKPj/H8xvo6BnyKhI5Jo1om9OXLZoFqfbsGHvbii4O7x5cujUdr3z5Wf+jQQC9Ea6tZ56AEsJGOjq597iTqTKRBX0QCSK8VkPZ2Z5NhTj655HiXjhn7VcJkExQdHVvydnR2B7MN75SAvviV7QLdGuOPktXKty5GenvNf7v+evOiJAijR2sbz2/LdmDG4mcwqXWV7410AK5eciOqoP+j3NK8gyJyQEReFJGMiBwbUX3KmzvXWblXXy358JInt/iesf/92U1s5VNkrC156+v8jRMvXb9N//h+Ngtcd53ecxZy331mF3qQLf5Sk/SKzchfvjyY/QkAoKtLy//Xyqeva/twrl5yJ6qgPxmAlearFsBUAAsBvCwi50dUp+La24HNDrcLLTOJz+8bXaAhuQmRTy1TGzGi1n9ur0A25nEz/8aPF18EJk8eyOKnW6FJetaFwNNPB5OSuBRNOQu+pimfPmAuJeXcJnfCDPr9AJ4EcBWAKQCOgRn4zwDwQwB9ABoAPCoiZxQ7iYhcKyIbRGTDjh07gq814LyVD7jOt+/W8ezGopjQteZ+6fptOPOf12g5FwzDXLcfxNh+ITt3Anv36ttW1grqGzcWnqRnzcjfpnkzIyd6enyN51s7iHZpyqcvALLfPI8B36XQgr5SaptS6pNKqfuVUr9XSu1RSnUppbJKqRsAXA5zG/k6AN8vcZ6fKqWalVLNY8eODb7ihuG8lT9sWNnxfD/YjUVxovMC9J29PXoCfyZj7gsfZK75QjZvBp55xrxfqFve6QY+Vuv+yisH/g/WLoDt7QMz8g8c0P9/yDd06EDmPevmcTzfyranc4vcKzXsBJlGsZm9r5RqA/BQ7tezReT4KOtzmNPurKqqkltLtmU78OVl7Z6rwZSSFDc6JvTZvbO3B1O/9ZT3i2NrcltUzjsP+NWvgBNOMFvj9u+OTGZgnf/GjcD06cBZZw1eZjd9urnPfX+/eRFhLbPr7QXuust8PEw+W/Z2urLt2XG2vjexCfo5K233A8y24cLatc7KDSk+vmnN2PcyilVXU82UkhRL1oQ+nfnwdnX14sZl7d7G+e2T2+yt1DAm9gFmy/y88waC9e23m2P97e3Af/zHwDr/OXPM3oj16wcuDFpbzX8rts/9wYPFHwuCiFlXTZn3dE3as3C2vndxC/rbbffrI6uF3cyZztJ8HjpU9CE/OfbZuqc4a5naiB/MaUJNld5UuEvXb8Ok1lXOZ/fnL2Gz58wPa2IfMHhpn1LmWP/cuYNn1G+x5Si4805gxIiBbvu4qKnRloRHdyImDnP6E7egb9+/sjOyWtitWzf4g1xMiZa+nzX5DPgUdy1TG7Fklv8UvYU8t3Wns8BfaAmbNds8mwXeekv/TnNObN5cek5QT4+5FC5uNHXtt2U7cKOPYc18HOb0z/+aG70usd3X907x44kngOMdTC/o6TFbFXn7bvtZhzzjpFGejyUKU8vURrRMbTy8BlvXkixgIG1vyS/6deuOXMJmD1xB7DSXRHV1wGuvHfE95tbCtk148PltjtpLTtw6h7lJdAmtpS8iJf9iIjIbwKW5X/9LKfVW8LVywE3mrbzusIVtm/Dc1p2ennbGSaPw4DVneTqWKCpWq7+uRu9Xy03L2kt3E2ezg2eZ5882L3RRQEfSsBZ/YdsmLF2vL+APr6liwNcozO79dhFZLiJXisiHRWS0iIwVkb8QkZ8C+AXMpZf7AXw5xHqVtnJl+TKWvO6wBz2ml3xj8YUM+FSxWqY24n8zn8JcjUuq+gEsWuFw6WwhVqa+oZWT+TsSGrr1daTVtfuXS0/Ter60C7N7vwbmWvzLS5R5C8AVSqmN4VSpDMMAOh1MLZg3D7jttkH/tLBtk6fZ+pobSESRsZZU6QoCvtd4s7VfWlOT79n6537/13rqkjN3+kS28jULM+h/AcBfAjgTQCOAMbnn3wlgI4DHAdynlNobYp1Ka211Nokv78q4Ldvh+Ytuyax4rFQk0uHbLVPw+o59noe58p3YugrH19dh/vkfdB8MCgW0IUPCT+QTNz6CfVu2A0ue3IK3OrsxrKYK3Zqy7QFmil2uxdcvzIx8jyilvqyU+phS6gSl1AilVK1S6n25TH0/ilXAB4DHHitfpsAHZv5yb3MQZ5w0ile1lDgPXnOWtq5+BXPN94JHNulZChbUrnyVoKrK7KX0mWWvo7MbCtAa8AGg08eqJyqOncmlOEl1uXr1oF/bsh3w8t7nxD1KMt0ttu7ePtyy0scYv8WaABhWrv446e8Hnn3W8+FBZNmz4z4jwWDQL6XXwZWmbXb/wrZNntekMuBT0vndijffrq5efOBrq9ji92roUHM/AA/ash3as+zZMQFPcBj0izEMZ+t6V60CYK7H9zqOr3t5E1EcLbp4svZz9vYDN5ZbzudENmsO1aWJx5n6VlrxoHC73GDFLTlPfDhdnz9+vK/1+ABwQPNYGFEctUxtxIY3d2pf0gUAX36o/fBzeGaNbdfVhbOLXZgaGsxtgH3SnWHPrr6uBosunsxgHzAG/WKcTOITAbJZ/HzBE76eimNXlBbfbpmC5hNG4WuPvKRtX3XAHJZf8Ii5SY/voGHfLbO2NhnL/HzMWbBm6AfZnd8wvAbZb54X2PlpAPuVCzEMYPfu8uVyy/n6fKSe4tgVpU3L1Eb8QXPyHsCc3LfkyS3lC7qRlOV848d7Oszqyg96/P7mi/QP/VBhDPqFXH+9s3Jjxvh+qsumNbI7i1KnLduB/3xB7+5rgLmcb+q3ntK3s1ulT/Czthj2uCzPzw6hTnADnfCxez+fYQAPP+ys7PjxvjbUAYD/enmHr+OJt++3hgAAGF9JREFUKlGQy712dfXixmXtuHFZu/9xYnuwHDYs3D3tdfCRVrct2+Frh9ByuIlONBj08zlt5U+ejCvn/dh3prG3Auw2I4qrsN73nd3mBcAtKzfj5osSPEmsQCpwL8IYvwfMFUuJ/VvEHLv37Vy08g+9+qqW1KKcxEdpFPb73mr9v3/BKkxqXYUZi59xPwTwhS/Ed8Men5vkAIMz7AXtO9xEJzJs6du52FLy019ZCvjsneQkPkqr+ed/EAse2RRoRrdC+nPD01YqX4uVP75kXv+4bdgj4iyXiEOLVmwO5e/BTXSixaBvt3at46KzVt+DTefN8/Q0AnjfNIQoAaz3vT3Y/tWHxuK/Xt4RSksTMGf7f3lZO4ZUy+HJavaLgSM+m/bx/alTgfZg1qs74rE73959Xy2CPqXQWF+HSaPr/O9i6EB9HTfRiZooH8vNotbc3Kw2bNig74Tz5gG33+6oaPeQoZj5xbuw46gGV0/ByStEpc1Y/Exogb+YahH0K1X+4jyq4O9hZzyr+z7s3hVLXU01Z+prIiIvKKWavRzLMX07Fy39KtWPf/zdzx2XFzDgEzkx//wPoq4m2g1w+pRytqOftWHPddfpHe+3ltopVfhWJuC3ZTswY/EzODE3f2Fh2yZ85aGNoQf8ahEIuDQvTti9bzdtGrDZ2c5dtX2HMK3jZcen/gEDPpEj9q7/qFv8wEDSn5KfX93j/T09wD33AN/4BjBunKtD81v0HZ3dgaQ+duJ7s0/n917MMOjbrVxZtogC8MDUC/BNl+P5fOMTOdcydXDSqg98bZWnLat1KbvEML/lXa7bf9gwM91vqXJ9febkYpdj90FveevUcC7LiyV271scpt4VwFULH4D2dKNEabNkVlPkX1aulvhZ3f7FblZ+f6tcoR3+XCbWsbr049A7AgDd3EgsltjSt2QyZZe/KAAf/YcHXE3emzt9ImerEvlktRhvWtaOKEKJAjB/+cZBddHKQ5rchW2b8PPn/4Q+pSAAqqoEff3xmZjNHCTxxNn7llNPLTue76Vr/43FF/qsGBHZnfv9X+OP2/dH9vwC4MrpE9F8wihn6/t9spbZ2Z8nqC2KdeFM/WD5mb3Plr7FwSQ+AXDmtt87PmUjr3SJtOvqibbbWAFYun7boKDb0dl9eJ95P4Gu0Dp6O/vzxElNtWDE0CHY3d3LHCQxx6BvWb68bBEF4PmJpzo+JbPtEekX5/0qrI1+LLVDqlAlxce3P3DsCOzY21MwMY6fLbuDJgIcM6yGQb4CMehbust/kbiZxMdUk0TBOL6+LjaT1co5eKh0r0SUwxReseu+sjHoA44yanVX1eCU+Y86PiUn7xEFI6q8/WRiwK9sUa+CiYc5c0o+rAAsP/1cx6err6vxWSEiKqZlaiO+c+kUNNbXHc72VsNvslA01tcx4Fc4tvQB4JVXSj7sdm3+oosn+6wQEZWSn7ynLduB+cs3ojdGS9aShruCJgODvmGUfFgBeOOYcbjwb3/o6HT1dTW8EiYKWdxS9yaF442HqGIw6Le2lnxYAEza/TbG7tvlKCnP7hC2pySiI9lb/1HvKJcEAubOTyKOhK1a5aiY0x31mIWKKHr2cX/yRoF7hiQRW/oTJgDvvVeyiJsxfY55EcVDfss/jklt4owXTMnElr6DnNebj32/ozH9huEczyeKo5apjZg7fSIk6opUCE7aSy629EtQAE786uOOytZUC26+iLP2ieLq2y1T0HzCKNyycjN2dXHuTb6G4TXo7GKGvaRj0NegYXgNbr5oMj8kRDFndfnbc9wTdwNNEwb9MsrN2ucuekSVh+P9JjZY0odj+jC78YtxOmufiCpTy9TG1Exas+Y0NNbX4dY5Tch+8zwG/JRhS78Et5n4iKgyJTmff2N9HZ5r/XjU1aCYYEsf5mS9SV99HA80fQoHq83roIPVQ3D/1AtKztpPS+uAKOkK5fOfO30iaqoqY75/tQhmnDQKdTXVg/6ds/ApH1v6OWP37cSs3z+N2r5DAIDavkOYtelX+PePfbbomD4/TETJkZ/PHwCaTxiFRSs2H97vvkqAOKX3z5+AZ01QfKuzm7PwqSAG/Zzrn/s5RA3e+7pK9eMff/dzfPO8eUeUn3HSKH6YiBKu0IUAEI8Nfurrao6YcV+svkSW1Af9tmwHAOCMt7YcbuVbavsOFRzT5/IWonSzb/BTqFV95R3r8NzWnQWPrakSHDVsCHZ19aJaBH1KQTAwodhJb0JdTTV38yRPRKkY9VW51NzcrDZs2ODrHDMWP3N4re7YfTvxoxX/ii9d/NWiXfqcFENETthzAVjBvdFjlzu77clORF5QSjV7OTb1LX17co7rn/s5PvKnzUW79AGO4xORMzq72tltT7qkfvZ+tZizc62JfFVQmLXpVxi7b9cRZUW46xQREVWu1Af9vtzwhn0inzWBL9+VZ04MtW5EREQ6pT7oN9bXFV2uZ2/tc/IeERFVutQH/fnnf7Dkcj0LAz4REVW61E/ka5naiM1llusNra6MrFxERESlpD7oAyiZahcA/vXy00OqCRERUXAi6d4XkRYR+aWIvCMiB0TkNRH5sYicFEV9SmkYXsMZ+0RElAihBn0x3QXgUQDnAzgWQC2AEwFcB6BdRC4Is04AUKr3/uaLmPWKiIiSIeyW/gIAX8jdfwjA6TAD/yUA3gBwFIBlInJymJX63uymgv8+d/pEtvKJiCgxQhvTF5HjAHwt9+sqAJ9RAzmAV4jIJgCbYAb+fwYwK6y6lcujTURElARhTuT7PIARuftfV3lJ/5VSr4vIHQBuBHCpiBynlHonrMoxzSURESVdmN37F+V+/lEptbFImYdzP6sAhD62T0RElGRhBv2puZ/PlyizAUBf7v4ZwVaHiIgoXUIJ+iLSCHOsHgBeK1ZOKXUQgJH79UNB14uIiChNwmrpj7Hd31Gm7Pbcz9EB1YWIiCiVwgr6I2z3D5Qpa21wf1TJUkRERORKWEHfnv5GFS01uGzBciJyrYhsEJENO3aU6zQgIiIiS1hBf5/tfl2ZssNyP/cXelAp9VOlVLNSqnns2LFaKkdERJQGYQX9d233y0Vq6/H3AqoLERFRKoUS9JVSHRho7Z9YrJyI1AI4Pvfry0HXi4iIKE3CXKefzf08s0SZaQCqc/dfDLY6RERE6RJmGt6VAP4SwMkiMkUptalAmctzP/sBPFHuhC+88MK7IvKmxjqOweChCIoH/l3ih3+TeOLfJX6C+Juc4PVAyUuBH5jchjuvARgOYKVS6uK8xycB+D3M5X0PK6VC23DHVocNSqnmsJ+XSuPfJX74N4kn/l3iJ25/k9C693Ob5/xz7teLROQXIjJFRMaKyF8DeAZmwN8H4Oth1YuIiCgtwuzeB4DvADgJwBcAzMnd7PYBmKOUeiXkehERESVemBP5oExXA7gUwJMwU/IeBPA6gJ8AaFJKlR3LD9BPI3xuKo5/l/jh3ySe+HeJn1j9TUIb0yciIqJohdrSJyIiougkMuiLSIuI/FJE3hGRAyLymoj8WERO0nDuo0XkmyLykojsFZFOEflvEblRRGp01D8pRKRORD4tIj8RkRdyr1WviOwQkadFZJ6IlEvLXOr8i0REObj9SOf/q5KJyCSHr9m+8mcr+Tz8nDgkIm84/JtYt79xeX5+TgoQ0ykicpWI3CYi/yMiB3OvRbmN4eznOU5E/lVEXhaRLhF5V0SeFZG/FREpfwZHz3GOiPyniLyVi2nbROR+EZnq+mRKqcTcYG7WcxfMzXoK3fYCuMDH+U8EsLXE+TcAaIj6dYjLDcCeEq+VdftfAB/weP5FDs6vAPwo6tciLjcAkxy+Zvt8PAc/J+5erzcc/k2s2zSX5+fnpPDrUuqzcMDhOZoBvFPiPKsB1Pqs580wc9cUOn8PgKvdnC9pLf0FMFcGAMBDAE4HcCyAS2B+sI4CsExETnZ7YhEZCjPB0Pthbv/7jwDGw/yCWwTzjzINwDI//4GEORrmRM2fA/gMzJUbowA0Abgd5pv2QwCeEhE/Wylvyz1XsdtNPs6dZBeg+Gt2nJcT8nPiyYdR+v07EkBHruz/KqVe8Pg8/JwU1wHgUQC/cXqAiIwBsAJmjHkPwFwA74P5nXZbrtgnAfy710qJyBUwPzcCc1n79NzzfQJAO4AaAP8hIjMdnzTqqy2NV23HwVzypwA8jtwkRdvjJ9oeX+7h/F/CwNXVrAKP/1/b4xdG/XrE4QbgRwCOK/H4V22v2f/1cP5FuWPfiPr/Wik3DG7dnBPA+fk50f+anm17zRZ4OJ6fk8Kvy9EwG4TjCrxWZVv6AL6bK9sHYHqBx3+ce7wfwBQP9RsG4E+5c2QB1OQ9Xg/zYkUB+B+n501SS//zMJP7AMDXVe5VsSilXgdwR+7XS3MZAt24Lvczq5RaXuDxH8Bcgmgvm2pKqS8pMylTMd/DwG6KnwqhShQ8fk70+1zupwKwNMqKJIlSaq9S6jGl1Ntuj83NS/m73K+PKaXWFyh2M4BemK30L3qo4kUwe8kA4GalVK/9QaVUJ4B/zf3aLCKOsv4lKehflPv5R6XUxiJlHs79rILZtemIiLwfZhec/RyD5P4gj+V+/YSIDHd6/rRSSh0C8Mfcr8eXKkvxx8+JfiIyDAN7kvxaKfWnKOtDh/0lgGNy94u913cAeDb368WFypRhxbQuFN+Lxv7cFxUpM0iSgr41i/H5EmU2wOyKAYAzXJx7mu1+qfNbjw0DcIqL86eZ1eOyx++JRKRKRMLOMlnxcuPwOvBzot/FGAgu9+s4IT8nWrh9r0/IzQHw8hwv5hpIR1DmtvXWfA9HMS0RQV9EGmFO0gPMTX0KUkodBGDkfv2Qi6ewT/wren6YmQUtbs6fSrnlJifmfi3UPebUsSKyGeZM1l4ReU9EVovIZ0WkutzBKfaj3NK8g7llQC+KSEZEjvV4Pn5O9LO69rsA/KfPc/Fzoo/1Xu8HUGqnV/t7/YNOTy4iVQD+T+7XUp8l+3M4+iwlIujD3LrQsqNoKdP23M/RAZx/u+2+m/On1ZLcTwV/qSrrYHYrW19co2DOmv0ZgGc8XGGnxWQMzIOphdlbthDAyyJyvofz8XOiUe59a/0d2pRSe32ekp8TfazXalexVniO1/f60QCsHjitMS0pQX+E7X65pArduZ9ulog5PX+37b6fJWiJJyLzYS47AYDblVKbPJymE+ZymPNhLhEbBvPDeAmAdbkyMwE8xpbMYf0w9724CsAUmF3HI2B2Df4Q5vBXA4BHRcTNEBjAz4lun4W5JAsAHvBxHn5O9LPe607jDRBMzLE/h6PzJ2Vcx571SBUtNbhsuXLFzq+rHqmVa0V+J/frJgD/5OU8SqlbC/zzQQArRGQVzPwAswB8DGY36b1enidJlFLbYLbu8mUBZEXkvwA8ArNV+H0A57g4PT8nes3N/XwbwBqvJ+HnJBBO44jX93pgMS0pLX17ytByaV2H5X7u93j+YUVLDX7MzflTQ0SmAVgOs4vxTzDXaneXPso9pVQfzCVhXbl/ukL3cySRUqoNZmIrADhbRNysquDnRJNcArGP5n79We79rB0/J55Z73Wn8QbwHnO0xrSkBP13bffHlilrPf5eyVLezm9/zM35UyH3RbYa5njVDgDnBbkESSn1HoDf5X5tCup5Emil7b6b142fE30+Z7vvp2u/LH5OPLHe6/VlVkJ4fa/vhTnhMv8cpZ7D0fkTEfRzyxasK6MTi5UTkVoMrAd/2cVTvGK7X/T8eY+5OX/iicgEmF2UY2Euz/ukUiqM18ia5FIfwnMlhX3ykZvXjZ8TDXKbtFhd+79XSrWH8LT8nLhjvderAUwsUc7+Xt/i9ORKqX4ArxY4R6nncPRZSkTQz8nmfp5Zosw0DMxcfdHFue25rkud33rsAMyNZAiAiIyFGfAnwpx0cpFSys3r78e43M/OkJ4vCcbZ7rt53fg50eMvYKZLBjStzXeAnxN33L7Xtyml3i1RrtRznFGsNyE3/GZl7XP0nZqkoG91SZ4sIlOKlLEyW/WjeIajIyilXgPwh7xzDJL7o1hZl55WSnUVKpc2IjISwC9hrlHtBXC5UmptSM89FubkJGDgopDKu8R233Erk58Tbayu/X6Yy+kCxc+JJ78BsDt3v9h7fQzMfROAwUNmTlnHjEDxNOX253b0HEkK+vdjYDLKP+c/KCKTAFyb+/WRMjnhC7k99/MMEbmswOM3YiC73O0FHk+dXArRlTCXg/UD+JxSyvHFVplzj8kN1xR7vAbmXgvWJJcHdTxvpcslsir1+GwAl+Z+/S+l1Fsun4KfEx9y7+lZuV+fzg1d+jkfPycByKWTvjP3a4uIfLRAsUUw19p7zUOyEgPZ9m7J/a0OE5FjYG5gBQAblFIbHJ016p2OdN4AfA0Du1H9AuY65LEA/hpmViMFc4LEyQWO/TVK7ESV++P9PlemC8A8mPMDTgDwTQCHco89FfXrEIcbzGGUx2x/jy/DXEda7Dbczd8EQAuAt2BuOHEezKGDY3I/PwOza8x67l8DqIr6NYnDDeYEyuUAroSZqGV07jPyFzC/mKx9u/cBON3N3yT3OD8n/v4+l9vet59zeAw/J95f7w/D3K7Wut2Zey0O5v37dAC1eceOyb22Kve5ugLmBe0HYOa8sF7XnxZ57nNsZf6mSJkrbWV+BXNFxxgAfwWzO1/lPlMzHf+fo37RNf8BBcBdthcp/7YXwAVFji35ZZYrcyKArSXOvwFAQ9SvQxxuGLyFq5PbEa+7gy8zJ+d9HEB91K9HXG4wx2zLvWYdAM4ucjw/J8H+fawL5X0ARjg8hp8T76/3rx2+PgrApALHNwN4p8Qxq5F3sWA79hxbub8pUcdFGLgYz7/1ALjazf85Kcl5AADKfIWuFpHHYW5leAaAkTCvxp4E8F2l1FYf539dRJpgtlovh5ndqg/mTM6fAfiRytv+kALzHMy92z8G4DQAx8LMJHcQ5t/7eQAPKKU8JzVJqC/A3CHsTACNMFsNQwDsBLAR5pf/fcpHyld+TrwRkdEYGLt9RCmlI4cBPycBUkptEJHTYCYYuxjABJiTlTcDuAfAvbm45Oc5FonIrwFcD+AsmOmTt8O8YPm+UsrVPAzxWR8iIiKqEEmayEdEREQlMOgTERGlBIM+ERFRSjDoExERpQSDPhERUUow6BMREaUEgz4REVFKMOgTERGlBIM+ERFRSjDoE1UgEVF+brbzLMr92xsR/neIKCQM+kRERCnBoE9UmY4ucrvAVubvS5QjohRK1C57RGmhlNpX6N9FpNv268Fi5WznWQRz604iSgG29ImIiFKCQZ8oxUpN5BORc2yT/yaJSIOI/D8ReUVEukTkTyJyt4hMsB1TLSLXisjzItIpIntE5GkROdtBXepF5Bsi8t8islNEDorImyJyv4g0af6vE6USu/eJyImJAO4DMMn2b+MB/C2Ac0VkBoDtAB4GcGHesR8HMFNELlFKPVHo5PL/27ufEJvCMI7j30dNTGkoI2K2ZpKVpoSyMWtlMcmfNAsLG8pabGyEbEY2s2JJsUDCsLLA7BArSSkpEgqLSa/FeW9dp+t27jWcON9Pnd573vPMnXc293efc+6cG7ENuAoMd/i9+4F9EXEkpXTud/8Qqcns9CVVcREYoAjgNXk7BMxThP8p4CQwARwF1lEE+A7gDUWDMRMRA+UnjogNwO1c/xTYQxH2K4AtwBWK16rpiCi/oZDUAzt9SVUsBzamlF61zZ2PiFXAcWBXntuZUrreVnMjIqaAWWAtxZuCW6XnngEGgSfA5pRS+4cRHwKTEXEBmALORMTNlFJCUs/s9CVVMV0K/JZLeVwE3C8Ffss94H1+vKn9QESMA1vz7sFS4Lc7lsf1gNf3pT4Z+pKquPOL+Zdtj2c7FeSuvFW3unR4ex4/A88jYmmnDfgIvMu1470vXxJ4el9SNW87TaaUvkVE15qs1cEPlubH8jgEfKq4lpUV6ySV2OlLquL7AtVEaX9ZH2tZ3MfPSMJOX1K9vuTxcUrJa/XSH2anL6lOrWv9YxFRPvUvaYEZ+pLq1Prw3xJgd50LkZrA0JdUm5TSA+BR3j0dEaPd6iNirNtxSd15TV9S3Q5Q3IRnGJiLiLPANeA1xWvUCMX/90/mcaimdUr/PENfUq1SSs8iYoLidrsjwIm8dfLhry1M+g95el9S7VJKc8AocBi4S/HlPfPAV+AFcBnYy89f+COpR+EtrCVJagY7fUmSGsLQlySpIQx9SZIawtCXJKkhDH1JkhrC0JckqSEMfUmSGsLQlySpIQx9SZIawtCXJKkhDH1JkhrC0JckqSF+AMIcTggS2K/gAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 作图\n",
    "dowhy.plotter.plot_treatment_outcome(df[data_dict[\"treatment_name\"]], df[data_dict[\"outcome_name\"]],\n",
    "                             df[data_dict[\"time_val\"]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:dowhy.causal_model:Causal Graph not provided. DoWhy will construct a graph based on data inputs.\n",
      "INFO:dowhy.causal_graph:If this is observed data (not from a randomized experiment), there might always be missing confounders. Adding a node named \"Unobserved Confounders\" to reflect this.\n",
      "INFO:dowhy.causal_model:Model to find the causal effect of treatment ['Treatment'] on outcome ['Outcome']\n",
      "WARNING:dowhy.causal_graph:Warning: Pygraphviz cannot be loaded. Check that graphviz and pygraphviz are installed.\n",
      "INFO:dowhy.causal_graph:Using Matplotlib for plotting\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 使用DoWhy分析干预是否会导致结果\n",
    "# step 1: 将问题建模为因果图\n",
    "model= CausalModel(\n",
    "        data=df,\n",
    "        treatment=data_dict[\"treatment_name\"],\n",
    "        outcome=data_dict[\"outcome_name\"],\n",
    "        common_causes=data_dict[\"common_causes_names\"],\n",
    "        instruments=data_dict[\"instrument_names\"])\n",
    "model.view_model(layout=\"dot\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 在图片causal_model.png中展示因果模型\n",
    "from IPython.display import Image, display\n",
    "display(Image(filename=\"causal_model.png\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_identifier:Common causes of treatment and outcome:['U', 'w0']\n",
      "WARNING:dowhy.causal_identifier:If this is observed data (not from a randomized experiment), there might always be missing confounders. Causal effect cannot be identified perfectly.\n",
      "INFO:dowhy.causal_identifier:Continuing by ignoring these unobserved confounders because proceed_when_unidentifiable flag is True.\n",
      "INFO:dowhy.causal_identifier:Instrumental variables for treatment and outcome:[]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimand type: nonparametric-ate\n",
      "### Estimand : 1\n",
      "Estimand name: backdoor\n",
      "Estimand expression:\n",
      "     d                               \n",
      "────────────(Expectation(Outcome|w0))\n",
      "d[Treatment]                         \n",
      "Estimand assumption 1, Unconfoundedness: If U→{Treatment} and U→Outcome then P(Outcome|Treatment,w0,U) = P(Outcome|Treatment,w0)\n",
      "### Estimand : 2\n",
      "Estimand name: iv\n",
      "No such variable found!\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# step2:使用形式因果图的特性来识别因果效应\n",
    "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n",
    "print(identified_estimand)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 4.145e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:37   Log-Likelihood:                 1867.5\n",
      "No. Observations:               10000   AIC:                            -3729.\n",
      "Df Residuals:                    9997   BIC:                            -3707.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0668      0.061     99.407      0.000       5.947       6.186\n",
      "x1             0.9883      0.010     97.170      0.000       0.968       1.008\n",
      "x2             1.0122      0.010     99.201      0.000       0.992       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        0.738   Durbin-Watson:                   2.009\n",
      "Prob(Omnibus):                  0.691   Jarque-Bera (JB):                0.703\n",
      "Skew:                           0.003   Prob(JB):                        0.704\n",
      "Kurtosis:                       3.041   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "Causal Estimate is 0.9882504484355463\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# step3: 估计因果关系\n",
    "# 一旦确定了上一步中识别得到的因果效应，便可以使用统计的方法来估计因果关系\n",
    "# 为了简单，使用线性回归的统计方式\n",
    "estimate = model.estimate_effect(identified_estimand,\n",
    "        method_name=\"backdoor.linear_regression\")\n",
    "print(\"Causal Estimate is \" + str(estimate.value))\n",
    "\n",
    "# Plot Slope of line between treamtent and outcome =causal effect\n",
    "dowhy.plotter.plot_causal_effect(estimate, df[data_dict[\"treatment_name\"]], df[data_dict[\"outcome_name\"]])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DoWhy estimate is 0.9882504484355463\n",
      "Actual true causal effect was 1\n"
     ]
    }
   ],
   "source": [
    "# 检查估计是否正确\n",
    "print(\"DoWhy estimate is \" + str(estimate.value))\n",
    "print (\"Actual true causal effect was {0}\".format(rvar))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0+w_random\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 2.763e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                 1867.7\n",
      "No. Observations:               10000   AIC:                            -3727.\n",
      "Df Residuals:                    9996   BIC:                            -3698.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0667      0.061     99.401      0.000       5.947       6.186\n",
      "x1             0.9883      0.010     97.168      0.000       0.968       1.008\n",
      "x2             1.0121      0.010     99.195      0.000       0.992       1.032\n",
      "x3            -0.0010      0.002     -0.503      0.615      -0.005       0.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.749   Durbin-Watson:                   2.009\n",
      "Prob(Omnibus):                  0.688   Jarque-Bera (JB):                0.713\n",
      "Skew:                           0.002   Prob(JB):                        0.700\n",
      "Kurtosis:                       3.041   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "Refute: Add a Random Common Cause\n",
      "Estimated effect:0.9882504484355463\n",
      "New effect:0.9882725760542064\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# step4:驳斥估计, 检查其是否符合假设，即进行敏感性分析\n",
    "# 添加随机的共同变量\n",
    "res_random=model.refute_estimate(identified_estimand, estimate, method_name=\"random_common_cause\")\n",
    "print(res_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_refuters.placebo_treatment_refuter:Refutation over 100 simulated datasets of permute treatment\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9971      0.006   1872.463      0.000      11.984      12.010\n",
      "x1            -0.0005      0.001     -0.548      0.583      -0.002       0.001\n",
      "x2             2.0013      0.001   2063.580      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.768   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.681   Jarque-Bera (JB):                0.732\n",
      "Skew:                           0.009   Prob(JB):                        0.694\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1456.9\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9879      0.006   1871.200      0.000      11.975      12.000\n",
      "x1             0.0010      0.001      1.035      0.301      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.630      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.814   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.666   Jarque-Bera (JB):                0.777\n",
      "Skew:                           0.009   Prob(JB):                        0.678\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.131e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1453.0\n",
      "No. Observations:               10000   AIC:                             2912.\n",
      "Df Residuals:                    9997   BIC:                             2934.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9767      0.006   1870.173      0.000      11.964      11.989\n",
      "x1             0.0029      0.001      2.984      0.003       0.001       0.005\n",
      "x2             2.0013      0.001   2064.424      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.908   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.635   Jarque-Bera (JB):                0.871\n",
      "Skew:                           0.012   Prob(JB):                        0.647\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9957      0.006   1872.243      0.000      11.983      12.008\n",
      "x1            -0.0003      0.001     -0.319      0.750      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.561      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.805   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.669   Jarque-Bera (JB):                0.768\n",
      "Skew:                           0.009   Prob(JB):                        0.681\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9909      0.006   1871.523      0.000      11.978      12.003\n",
      "x1             0.0005      0.001      0.522      0.602      -0.001       0.002\n",
      "x2             2.0013      0.001   2063.585      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.806   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.668   Jarque-Bera (JB):                0.769\n",
      "Skew:                           0.009   Prob(JB):                        0.681\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9901      0.006   1871.192      0.000      11.978      12.003\n",
      "x1             0.0006      0.001      0.654      0.513      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.416      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.773   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.680   Jarque-Bera (JB):                0.736\n",
      "Skew:                           0.009   Prob(JB):                        0.692\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9943      0.006   1871.968      0.000      11.982      12.007\n",
      "x1         -7.029e-05      0.001     -0.073      0.942      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.520      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.791   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.673   Jarque-Bera (JB):                0.755\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9949      0.006   1872.164      0.000      11.982      12.007\n",
      "x1            -0.0002      0.001     -0.174      0.862      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.420      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.782   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.745\n",
      "Skew:                           0.009   Prob(JB):                        0.689\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9903      0.006   1871.163      0.000      11.978      12.003\n",
      "x1             0.0006      0.001      0.625      0.532      -0.001       0.002\n",
      "x2             2.0013      0.001   2063.362      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.789   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.752\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9977      0.006   1872.514      0.000      11.985      12.010\n",
      "x1            -0.0006      0.001     -0.663      0.507      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.550      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.821   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.663   Jarque-Bera (JB):                0.785\n",
      "Skew:                           0.009   Prob(JB):                        0.675\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1455.7\n",
      "No. Observations:               10000   AIC:                             2917.\n",
      "Df Residuals:                    9997   BIC:                             2939.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0048      0.006   1874.051      0.000      11.992      12.017\n",
      "x1            -0.0018      0.001     -1.889      0.059      -0.004    6.92e-05\n",
      "x2             2.0013      0.001   2063.807      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.787   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.750\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9900      0.006   1871.470      0.000      11.977      12.003\n",
      "x1             0.0006      0.001      0.671      0.502      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.583      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.731   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.694   Jarque-Bera (JB):                0.695\n",
      "Skew:                           0.008   Prob(JB):                        0.707\n",
      "Kurtosis:                       3.037   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9934      0.006   1871.939      0.000      11.981      12.006\n",
      "x1          8.036e-05      0.001      0.083      0.934      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.444      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.786   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.750\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1456.8\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0005      0.006   1873.193      0.000      11.988      12.013\n",
      "x1            -0.0011      0.001     -1.153      0.249      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.652      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.720   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.698   Jarque-Bera (JB):                0.683\n",
      "Skew:                           0.009   Prob(JB):                        0.711\n",
      "Kurtosis:                       3.036   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9935      0.006   1871.896      0.000      11.981      12.006\n",
      "x1          5.947e-05      0.001      0.062      0.951      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.293      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.788   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.751\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9921      0.006   1871.752      0.000      11.980      12.005\n",
      "x1             0.0003      0.001      0.309      0.757      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.575      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.791   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.673   Jarque-Bera (JB):                0.755\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9920      0.006   1871.648      0.000      11.979      12.005\n",
      "x1             0.0003      0.001      0.329      0.742      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.550      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.780   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.677   Jarque-Bera (JB):                0.743\n",
      "Skew:                           0.009   Prob(JB):                        0.690\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9975      0.006   1872.481      0.000      11.985      12.010\n",
      "x1            -0.0006      0.001     -0.626      0.531      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.549      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.771   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.680   Jarque-Bera (JB):                0.735\n",
      "Skew:                           0.009   Prob(JB):                        0.693\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9925      0.006   1871.718      0.000      11.980      12.005\n",
      "x1             0.0002      0.001      0.243      0.808      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.544      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.783   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.746\n",
      "Skew:                           0.009   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9965      0.006   1872.271      0.000      11.984      12.009\n",
      "x1            -0.0004      0.001     -0.459      0.646      -0.002       0.001\n",
      "x2             2.0013      0.001   2063.496      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.779   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.677   Jarque-Bera (JB):                0.742\n",
      "Skew:                           0.009   Prob(JB):                        0.690\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:38   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9913      0.006   1871.645      0.000      11.979      12.004\n",
      "x1             0.0004      0.001      0.451      0.652      -0.001       0.002\n",
      "x2             2.0013      0.001   2063.549      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.772   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.680   Jarque-Bera (JB):                0.735\n",
      "Skew:                           0.009   Prob(JB):                        0.692\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9894      0.006   1871.343      0.000      11.977      12.002\n",
      "x1             0.0007      0.001      0.774      0.439      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.436      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.809   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.667   Jarque-Bera (JB):                0.773\n",
      "Skew:                           0.009   Prob(JB):                        0.679\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1455.4\n",
      "No. Observations:               10000   AIC:                             2917.\n",
      "Df Residuals:                    9997   BIC:                             2938.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0056      0.006   1873.974      0.000      11.993      12.018\n",
      "x1            -0.0020      0.001     -2.025      0.043      -0.004   -6.22e-05\n",
      "x2             2.0013      0.001   2063.856      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.911   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.634   Jarque-Bera (JB):                0.875\n",
      "Skew:                           0.010   Prob(JB):                        0.646\n",
      "Kurtosis:                       3.042   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.0\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9997      0.006   1873.023      0.000      11.987      12.012\n",
      "x1            -0.0010      0.001     -0.999      0.318      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.613      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.794   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.672   Jarque-Bera (JB):                0.758\n",
      "Skew:                           0.009   Prob(JB):                        0.685\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9915      0.006   1871.671      0.000      11.979      12.004\n",
      "x1             0.0004      0.001      0.415      0.678      -0.001       0.002\n",
      "x2             2.0013      0.001   2063.522      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.788   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.751\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1456.4\n",
      "No. Observations:               10000   AIC:                             2919.\n",
      "Df Residuals:                    9997   BIC:                             2940.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0022      0.006   1873.514      0.000      11.990      12.015\n",
      "x1            -0.0014      0.001     -1.434      0.152      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.720      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.765   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.682   Jarque-Bera (JB):                0.728\n",
      "Skew:                           0.011   Prob(JB):                        0.695\n",
      "Kurtosis:                       3.036   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1456.9\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0000      0.006   1873.097      0.000      11.987      12.013\n",
      "x1            -0.0010      0.001     -1.067      0.286      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.658      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.795   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.672   Jarque-Bera (JB):                0.758\n",
      "Skew:                           0.010   Prob(JB):                        0.685\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9894      0.006   1871.103      0.000      11.977      12.002\n",
      "x1             0.0008      0.001      0.776      0.438      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.437      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.783   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.746\n",
      "Skew:                           0.009   Prob(JB):                        0.689\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1456.9\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9879      0.006   1870.941      0.000      11.975      12.000\n",
      "x1             0.0010      0.001      1.044      0.297      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.515      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.757   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.685   Jarque-Bera (JB):                0.720\n",
      "Skew:                           0.009   Prob(JB):                        0.698\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9977      0.006   1872.333      0.000      11.985      12.010\n",
      "x1            -0.0006      0.001     -0.659      0.510      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.396      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.789   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.753\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9936      0.006   1871.976      0.000      11.981      12.006\n",
      "x1           5.35e-05      0.001      0.055      0.956      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.560      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.785   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.749\n",
      "Skew:                           0.009   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9906      0.006   1871.532      0.000      11.978      12.003\n",
      "x1             0.0005      0.001      0.567      0.571      -0.001       0.002\n",
      "x2             2.0013      0.001   2063.602      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.780   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.677   Jarque-Bera (JB):                0.744\n",
      "Skew:                           0.009   Prob(JB):                        0.689\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9973      0.006   1872.597      0.000      11.985      12.010\n",
      "x1            -0.0006      0.001     -0.596      0.551      -0.002       0.001\n",
      "x2             2.0013      0.001   2063.527      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.790   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.754\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9955      0.006   1872.273      0.000      11.983      12.008\n",
      "x1            -0.0003      0.001     -0.279      0.781      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.454      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.782   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.745\n",
      "Skew:                           0.009   Prob(JB):                        0.689\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1456.1\n",
      "No. Observations:               10000   AIC:                             2918.\n",
      "Df Residuals:                    9997   BIC:                             2940.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9844      0.006   1870.720      0.000      11.972      11.997\n",
      "x1             0.0016      0.001      1.644      0.100      -0.000       0.003\n",
      "x2             2.0013      0.001   2063.820      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.760   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.684   Jarque-Bera (JB):                0.724\n",
      "Skew:                           0.009   Prob(JB):                        0.696\n",
      "Kurtosis:                       3.037   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9910      0.006   1871.247      0.000      11.978      12.004\n",
      "x1             0.0005      0.001      0.498      0.618      -0.001       0.002\n",
      "x2             2.0013      0.001   2062.807      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.801   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.670   Jarque-Bera (JB):                0.765\n",
      "Skew:                           0.009   Prob(JB):                        0.682\n",
      "Kurtosis:                       3.039   Cond. No.                         15.5\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1456.8\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0008      0.006   1873.159      0.000      11.988      12.013\n",
      "x1            -0.0012      0.001     -1.193      0.233      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.704      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.805   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.669   Jarque-Bera (JB):                0.769\n",
      "Skew:                           0.009   Prob(JB):                        0.681\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9916      0.006   1871.650      0.000      11.979      12.004\n",
      "x1             0.0004      0.001      0.393      0.694      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.583      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.807   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.668   Jarque-Bera (JB):                0.771\n",
      "Skew:                           0.009   Prob(JB):                        0.680\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.0\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9992      0.006   1872.702      0.000      11.987      12.012\n",
      "x1            -0.0009      0.001     -0.927      0.354      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.524      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.770   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.680   Jarque-Bera (JB):                0.734\n",
      "Skew:                           0.008   Prob(JB):                        0.693\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1456.8\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0005      0.006   1873.156      0.000      11.988      12.013\n",
      "x1            -0.0011      0.001     -1.138      0.255      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.558      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.756   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.685   Jarque-Bera (JB):                0.719\n",
      "Skew:                           0.009   Prob(JB):                        0.698\n",
      "Kurtosis:                       3.037   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1455.7\n",
      "No. Observations:               10000   AIC:                             2917.\n",
      "Df Residuals:                    9997   BIC:                             2939.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0047      0.006   1873.609      0.000      11.992      12.017\n",
      "x1            -0.0018      0.001     -1.867      0.062      -0.004    9.01e-05\n",
      "x2             2.0013      0.001   2063.640      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.839   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.658   Jarque-Bera (JB):                0.803\n",
      "Skew:                           0.009   Prob(JB):                        0.669\n",
      "Kurtosis:                       3.040   Cond. No.                         15.5\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1456.9\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0002      0.006   1873.054      0.000      11.988      12.013\n",
      "x1            -0.0011      0.001     -1.102      0.271      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.680      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.790   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.754\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9899      0.006   1871.456      0.000      11.977      12.002\n",
      "x1             0.0007      0.001      0.687      0.492      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.602      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.787   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.750\n",
      "Skew:                           0.010   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9975      0.006   1872.470      0.000      11.985      12.010\n",
      "x1            -0.0006      0.001     -0.623      0.533      -0.002       0.001\n",
      "x2             2.0013      0.001   2063.161      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.774   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.679   Jarque-Bera (JB):                0.738\n",
      "Skew:                           0.009   Prob(JB):                        0.691\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9931      0.006   1871.883      0.000      11.981      12.006\n",
      "x1             0.0001      0.001      0.133      0.894      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.571      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.792   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.673   Jarque-Bera (JB):                0.756\n",
      "Skew:                           0.009   Prob(JB):                        0.685\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9949      0.006   1872.193      0.000      11.982      12.007\n",
      "x1            -0.0002      0.001     -0.178      0.858      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.552      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.785   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.749\n",
      "Skew:                           0.009   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1456.3\n",
      "No. Observations:               10000   AIC:                             2919.\n",
      "Df Residuals:                    9997   BIC:                             2940.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9851      0.006   1870.767      0.000      11.973      11.998\n",
      "x1             0.0015      0.001      1.525      0.127      -0.000       0.003\n",
      "x2             2.0013      0.001   2063.763      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.715   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.699   Jarque-Bera (JB):                0.678\n",
      "Skew:                           0.009   Prob(JB):                        0.712\n",
      "Kurtosis:                       3.036   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9965      0.006   1872.457      0.000      11.984      12.009\n",
      "x1            -0.0004      0.001     -0.451      0.652      -0.002       0.001\n",
      "x2             2.0013      0.001   2063.553      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.782   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.746\n",
      "Skew:                           0.009   Prob(JB):                        0.689\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:39   Log-Likelihood:                -1457.1\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9985      0.006   1872.607      0.000      11.986      12.011\n",
      "x1            -0.0008      0.001     -0.796      0.426      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.537      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.778   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.678   Jarque-Bera (JB):                0.742\n",
      "Skew:                           0.009   Prob(JB):                        0.690\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9984      0.006   1872.450      0.000      11.986      12.011\n",
      "x1            -0.0008      0.001     -0.779      0.436      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.410      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.783   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.747\n",
      "Skew:                           0.009   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9960      0.006   1872.139      0.000      11.983      12.009\n",
      "x1            -0.0004      0.001     -0.372      0.710      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.446      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.803   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.669   Jarque-Bera (JB):                0.767\n",
      "Skew:                           0.009   Prob(JB):                        0.682\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9931      0.006   1871.880      0.000      11.981      12.006\n",
      "x1             0.0001      0.001      0.140      0.888      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.421      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.786   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.750\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9939      0.006   1871.817      0.000      11.981      12.006\n",
      "x1          -1.15e-06      0.001     -0.001      0.999      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.449      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.789   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.752\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1455.8\n",
      "No. Observations:               10000   AIC:                             2918.\n",
      "Df Residuals:                    9997   BIC:                             2939.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9834      0.006   1870.620      0.000      11.971      11.996\n",
      "x1             0.0018      0.001      1.823      0.068      -0.000       0.004\n",
      "x2             2.0013      0.001   2063.885      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.784   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.747\n",
      "Skew:                           0.009   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.0\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9882      0.006   1871.186      0.000      11.976      12.001\n",
      "x1             0.0010      0.001      0.986      0.324      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.663      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.824   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.662   Jarque-Bera (JB):                0.788\n",
      "Skew:                           0.008   Prob(JB):                        0.674\n",
      "Kurtosis:                       3.040   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9982      0.006   1872.719      0.000      11.986      12.011\n",
      "x1            -0.0007      0.001     -0.741      0.459      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.626      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.812   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.666   Jarque-Bera (JB):                0.775\n",
      "Skew:                           0.009   Prob(JB):                        0.679\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.1\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9989      0.006   1872.747      0.000      11.986      12.011\n",
      "x1            -0.0008      0.001     -0.875      0.382      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.595      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.784   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.747\n",
      "Skew:                           0.008   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1455.9\n",
      "No. Observations:               10000   AIC:                             2918.\n",
      "Df Residuals:                    9997   BIC:                             2939.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9836      0.006   1870.652      0.000      11.971      11.996\n",
      "x1             0.0017      0.001      1.788      0.074      -0.000       0.004\n",
      "x2             2.0013      0.001   2063.880      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.812   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.666   Jarque-Bera (JB):                0.776\n",
      "Skew:                           0.008   Prob(JB):                        0.678\n",
      "Kurtosis:                       3.040   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9947      0.006   1872.028      0.000      11.982      12.007\n",
      "x1            -0.0001      0.001     -0.133      0.895      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.526      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.792   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.673   Jarque-Bera (JB):                0.756\n",
      "Skew:                           0.009   Prob(JB):                        0.685\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9945      0.006   1872.123      0.000      11.982      12.007\n",
      "x1         -9.953e-05      0.001     -0.103      0.918      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.550      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.786   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.749\n",
      "Skew:                           0.009   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1455.7\n",
      "No. Observations:               10000   AIC:                             2917.\n",
      "Df Residuals:                    9997   BIC:                             2939.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9829      0.006   1870.436      0.000      11.970      11.995\n",
      "x1             0.0018      0.001      1.902      0.057   -5.61e-05       0.004\n",
      "x2             2.0013      0.001   2063.429      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.863   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.649   Jarque-Bera (JB):                0.828\n",
      "Skew:                           0.009   Prob(JB):                        0.661\n",
      "Kurtosis:                       3.041   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9929      0.006   1871.694      0.000      11.980      12.005\n",
      "x1             0.0002      0.001      0.173      0.862      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.477      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.795   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.672   Jarque-Bera (JB):                0.759\n",
      "Skew:                           0.009   Prob(JB):                        0.684\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9899      0.006   1871.274      0.000      11.977      12.002\n",
      "x1             0.0007      0.001      0.693      0.488      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.523      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.849   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.654   Jarque-Bera (JB):                0.813\n",
      "Skew:                           0.010   Prob(JB):                        0.666\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9919      0.006   1871.713      0.000      11.979      12.004\n",
      "x1             0.0003      0.001      0.355      0.722      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.578      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.800   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.670   Jarque-Bera (JB):                0.763\n",
      "Skew:                           0.009   Prob(JB):                        0.683\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.1\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9891      0.006   1871.340      0.000      11.977      12.002\n",
      "x1             0.0008      0.001      0.834      0.404      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.634      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.820   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.664   Jarque-Bera (JB):                0.784\n",
      "Skew:                           0.009   Prob(JB):                        0.676\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9984      0.006   1872.784      0.000      11.986      12.011\n",
      "x1            -0.0008      0.001     -0.777      0.437      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.556      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.784   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.747\n",
      "Skew:                           0.009   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9950      0.006   1872.211      0.000      11.982      12.008\n",
      "x1            -0.0002      0.001     -0.195      0.845      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.532      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.791   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.673   Jarque-Bera (JB):                0.754\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1456.4\n",
      "No. Observations:               10000   AIC:                             2919.\n",
      "Df Residuals:                    9997   BIC:                             2940.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0022      0.006   1873.531      0.000      11.990      12.015\n",
      "x1            -0.0014      0.001     -1.448      0.148      -0.003       0.000\n",
      "x2             2.0013      0.001   2063.732      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.850   Durbin-Watson:                   2.002\n",
      "Prob(Omnibus):                  0.654   Jarque-Bera (JB):                0.814\n",
      "Skew:                           0.009   Prob(JB):                        0.666\n",
      "Kurtosis:                       3.040   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9982      0.006   1872.686      0.000      11.986      12.011\n",
      "x1            -0.0007      0.001     -0.753      0.451      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.615      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.751   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.687   Jarque-Bera (JB):                0.715\n",
      "Skew:                           0.009   Prob(JB):                        0.700\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9921      0.006   1871.603      0.000      11.980      12.005\n",
      "x1             0.0003      0.001      0.310      0.757      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.504      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.793   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.673   Jarque-Bera (JB):                0.757\n",
      "Skew:                           0.009   Prob(JB):                        0.685\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9927      0.006   1871.843      0.000      11.980      12.005\n",
      "x1             0.0002      0.001      0.200      0.841      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.570      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.791   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.673   Jarque-Bera (JB):                0.754\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9894      0.006   1871.020      0.000      11.977      12.002\n",
      "x1             0.0007      0.001      0.775      0.438      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.354      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.835   Durbin-Watson:                   2.004\n",
      "Prob(Omnibus):                  0.659   Jarque-Bera (JB):                0.799\n",
      "Skew:                           0.009   Prob(JB):                        0.671\n",
      "Kurtosis:                       3.040   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9985      0.006   1872.654      0.000      11.986      12.011\n",
      "x1            -0.0008      0.001     -0.790      0.429      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.577      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.789   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.753\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9934      0.006   1871.901      0.000      11.981      12.006\n",
      "x1          8.842e-05      0.001      0.091      0.927      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.365      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.787   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.750\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9939      0.006   1872.026      0.000      11.981      12.006\n",
      "x1          5.592e-06      0.001      0.006      0.995      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.519      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.789   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.752\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:40   Log-Likelihood:                -1456.8\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0005      0.006   1873.141      0.000      11.988      12.013\n",
      "x1            -0.0011      0.001     -1.140      0.254      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.704      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.730   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.694   Jarque-Bera (JB):                0.694\n",
      "Skew:                           0.009   Prob(JB):                        0.707\n",
      "Kurtosis:                       3.037   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1456.6\n",
      "No. Observations:               10000   AIC:                             2919.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9861      0.006   1870.985      0.000      11.974      11.999\n",
      "x1             0.0013      0.001      1.351      0.177      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.699      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.804   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.669   Jarque-Bera (JB):                0.768\n",
      "Skew:                           0.009   Prob(JB):                        0.681\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9972      0.006   1872.552      0.000      11.985      12.010\n",
      "x1            -0.0006      0.001     -0.576      0.565      -0.002       0.001\n",
      "x2             2.0013      0.001   2063.441      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.797   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.671   Jarque-Bera (JB):                0.761\n",
      "Skew:                           0.009   Prob(JB):                        0.684\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9900      0.006   1871.326      0.000      11.977      12.003\n",
      "x1             0.0006      0.001      0.670      0.503      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.219      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.784   Durbin-Watson:                   2.002\n",
      "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.748\n",
      "Skew:                           0.009   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9926      0.006   1871.838      0.000      11.980      12.005\n",
      "x1             0.0002      0.001      0.218      0.827      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.554      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.798   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.671   Jarque-Bera (JB):                0.761\n",
      "Skew:                           0.009   Prob(JB):                        0.683\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9897      0.006   1871.356      0.000      11.977      12.002\n",
      "x1             0.0007      0.001      0.726      0.468      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.607      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.797   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.671   Jarque-Bera (JB):                0.761\n",
      "Skew:                           0.009   Prob(JB):                        0.684\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9903      0.006   1871.462      0.000      11.978      12.003\n",
      "x1             0.0006      0.001      0.631      0.528      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.435      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.768   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.681   Jarque-Bera (JB):                0.732\n",
      "Skew:                           0.009   Prob(JB):                        0.694\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9943      0.006   1871.864      0.000      11.982      12.007\n",
      "x1         -7.294e-05      0.001     -0.075      0.940      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.433      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.789   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.752\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.3\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9968      0.006   1872.395      0.000      11.984      12.009\n",
      "x1            -0.0005      0.001     -0.501      0.616      -0.002       0.001\n",
      "x2             2.0013      0.001   2063.244      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.788   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.752\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1456.8\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0004      0.006   1872.877      0.000      11.988      12.013\n",
      "x1            -0.0011      0.001     -1.128      0.259      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.530      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.796   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.672   Jarque-Bera (JB):                0.760\n",
      "Skew:                           0.008   Prob(JB):                        0.684\n",
      "Kurtosis:                       3.040   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.2\n",
      "No. Observations:               10000   AIC:                             2920.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9983      0.006   1872.763      0.000      11.986      12.011\n",
      "x1            -0.0007      0.001     -0.757      0.449      -0.003       0.001\n",
      "x2             2.0013      0.001   2063.611      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.816   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.665   Jarque-Bera (JB):                0.780\n",
      "Skew:                           0.009   Prob(JB):                        0.677\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9960      0.006   1872.147      0.000      11.983      12.009\n",
      "x1            -0.0004      0.001     -0.370      0.711      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.455      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.791   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.673   Jarque-Bera (JB):                0.755\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1454.8\n",
      "No. Observations:               10000   AIC:                             2916.\n",
      "Df Residuals:                    9997   BIC:                             2937.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         12.0072      0.006   1874.560      0.000      11.995      12.020\n",
      "x1            -0.0022      0.001     -2.303      0.021      -0.004      -0.000\n",
      "x2             2.0013      0.001   2064.118      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.836   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.658   Jarque-Bera (JB):                0.800\n",
      "Skew:                           0.008   Prob(JB):                        0.670\n",
      "Kurtosis:                       3.040   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9935      0.006   1871.974      0.000      11.981      12.006\n",
      "x1          5.988e-05      0.001      0.062      0.951      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.551      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.786   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.750\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9913      0.006   1871.604      0.000      11.979      12.004\n",
      "x1             0.0004      0.001      0.449      0.653      -0.001       0.002\n",
      "x2             2.0013      0.001   2063.588      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.796   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.672   Jarque-Bera (JB):                0.759\n",
      "Skew:                           0.009   Prob(JB):                        0.684\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1456.5\n",
      "No. Observations:               10000   AIC:                             2919.\n",
      "Df Residuals:                    9997   BIC:                             2941.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9858      0.006   1870.946      0.000      11.973      11.998\n",
      "x1             0.0014      0.001      1.402      0.161      -0.001       0.003\n",
      "x2             2.0013      0.001   2063.769      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.721   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.697   Jarque-Bera (JB):                0.684\n",
      "Skew:                           0.009   Prob(JB):                        0.710\n",
      "Kurtosis:                       3.036   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9952      0.006   1871.716      0.000      11.983      12.008\n",
      "x1            -0.0002      0.001     -0.224      0.823      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.160      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.794   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.672   Jarque-Bera (JB):                0.757\n",
      "Skew:                           0.009   Prob(JB):                        0.685\n",
      "Kurtosis:                       3.038   Cond. No.                         15.5\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9965      0.006   1872.211      0.000      11.984      12.009\n",
      "x1            -0.0004      0.001     -0.450      0.653      -0.002       0.001\n",
      "x2             2.0013      0.001   2063.451      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.791   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.673   Jarque-Bera (JB):                0.754\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.039   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9953      0.006   1872.225      0.000      11.983      12.008\n",
      "x1            -0.0002      0.001     -0.249      0.804      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.399      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.785   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.748\n",
      "Skew:                           0.009   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9924      0.006   1871.808      0.000      11.980      12.005\n",
      "x1             0.0002      0.001      0.254      0.799      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.550      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.780   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.677   Jarque-Bera (JB):                0.743\n",
      "Skew:                           0.009   Prob(JB):                        0.690\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1456.0\n",
      "No. Observations:               10000   AIC:                             2918.\n",
      "Df Residuals:                    9997   BIC:                             2940.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9840      0.006   1870.763      0.000      11.971      11.997\n",
      "x1             0.0017      0.001      1.717      0.086      -0.000       0.004\n",
      "x2             2.0013      0.001   2063.854      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.790   Durbin-Watson:                   2.004\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.754\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9934      0.006   1871.929      0.000      11.981      12.006\n",
      "x1          8.816e-05      0.001      0.091      0.927      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.570      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.788   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.751\n",
      "Skew:                           0.009   Prob(JB):                        0.687\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.130e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1454.5\n",
      "No. Observations:               10000   AIC:                             2915.\n",
      "Df Residuals:                    9997   BIC:                             2937.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9800      0.006   1870.398      0.000      11.967      11.993\n",
      "x1             0.0023      0.001      2.420      0.016       0.000       0.004\n",
      "x2             2.0013      0.001   2064.117      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.906   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.636   Jarque-Bera (JB):                0.870\n",
      "Skew:                           0.010   Prob(JB):                        0.647\n",
      "Kurtosis:                       3.041   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.4\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2942.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9953      0.006   1872.257      0.000      11.983      12.008\n",
      "x1            -0.0002      0.001     -0.247      0.805      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.504      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.785   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.675   Jarque-Bera (JB):                0.748\n",
      "Skew:                           0.009   Prob(JB):                        0.688\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~placebo+w0\n",
      "INFO:dowhy.causal_refuters.placebo_treatment_refuter:Making use of Bootstrap as we have more than 100 examples.\n",
      "                 Note: The greater the number of examples, the more accurate are the confidence estimates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.129e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                -1457.5\n",
      "No. Observations:               10000   AIC:                             2921.\n",
      "Df Residuals:                    9997   BIC:                             2943.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         11.9938      0.006   1871.876      0.000      11.981      12.006\n",
      "x1          1.001e-05      0.001      0.010      0.992      -0.002       0.002\n",
      "x2             2.0013      0.001   2063.507      0.000       1.999       2.003\n",
      "==============================================================================\n",
      "Omnibus:                        0.789   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.674   Jarque-Bera (JB):                0.753\n",
      "Skew:                           0.009   Prob(JB):                        0.686\n",
      "Kurtosis:                       3.038   Cond. No.                         15.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "Refute: Use a Placebo Treatment\n",
      "Estimated effect:0.9882504484355463\n",
      "New effect:3.2129067940012134e-06\n",
      "p value:0.49\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 使用随机变量代替treatment(干预)\n",
    "res_placebo=model.refute_estimate(identified_estimand, estimate,\n",
    "        method_name=\"placebo_treatment_refuter\", placebo_type=\"permute\")\n",
    "print(res_placebo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_refuters.data_subset_refuter:Refutation over 0.9 simulated datasets of size 9000.0 each\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.745e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                 1714.2\n",
      "No. Observations:                9000   AIC:                            -3422.\n",
      "Df Residuals:                    8997   BIC:                            -3401.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0765      0.064     95.004      0.000       5.951       6.202\n",
      "x1             0.9865      0.011     92.557      0.000       0.966       1.007\n",
      "x2             1.0139      0.011     94.838      0.000       0.993       1.035\n",
      "==============================================================================\n",
      "Omnibus:                        0.077   Durbin-Watson:                   1.977\n",
      "Prob(Omnibus):                  0.962   Jarque-Bera (JB):                0.057\n",
      "Skew:                           0.001   Prob(JB):                        0.972\n",
      "Kurtosis:                       3.012   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.739e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                 1692.5\n",
      "No. Observations:                9000   AIC:                            -3379.\n",
      "Df Residuals:                    8997   BIC:                            -3358.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0677      0.065     93.985      0.000       5.941       6.194\n",
      "x1             0.9882      0.011     91.846      0.000       0.967       1.009\n",
      "x2             1.0117      0.011     93.739      0.000       0.991       1.033\n",
      "==============================================================================\n",
      "Omnibus:                        0.689   Durbin-Watson:                   2.022\n",
      "Prob(Omnibus):                  0.709   Jarque-Bera (JB):                0.651\n",
      "Skew:                           0.003   Prob(JB):                        0.722\n",
      "Kurtosis:                       3.041   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.735e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:41   Log-Likelihood:                 1674.0\n",
      "No. Observations:                9000   AIC:                            -3342.\n",
      "Df Residuals:                    8997   BIC:                            -3321.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0606      0.064     94.086      0.000       5.934       6.187\n",
      "x1             0.9893      0.011     92.167      0.000       0.968       1.010\n",
      "x2             1.0108      0.011     93.871      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        0.720   Durbin-Watson:                   1.974\n",
      "Prob(Omnibus):                  0.698   Jarque-Bera (JB):                0.683\n",
      "Skew:                          -0.001   Prob(JB):                        0.711\n",
      "Kurtosis:                       3.043   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.715e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1683.0\n",
      "No. Observations:                9000   AIC:                            -3360.\n",
      "Df Residuals:                    8997   BIC:                            -3339.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0517      0.064     94.247      0.000       5.926       6.178\n",
      "x1             0.9908      0.011     92.599      0.000       0.970       1.012\n",
      "x2             1.0097      0.011     94.041      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        1.619   Durbin-Watson:                   1.985\n",
      "Prob(Omnibus):                  0.445   Jarque-Bera (JB):                1.617\n",
      "Skew:                          -0.005   Prob(JB):                        0.446\n",
      "Kurtosis:                       3.065   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.722e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1678.5\n",
      "No. Observations:                9000   AIC:                            -3351.\n",
      "Df Residuals:                    8997   BIC:                            -3330.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0796      0.064     94.781      0.000       5.954       6.205\n",
      "x1             0.9860      0.011     92.248      0.000       0.965       1.007\n",
      "x2             1.0148      0.011     94.629      0.000       0.994       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        0.900   Durbin-Watson:                   1.960\n",
      "Prob(Omnibus):                  0.637   Jarque-Bera (JB):                0.865\n",
      "Skew:                           0.007   Prob(JB):                        0.649\n",
      "Kurtosis:                       3.046   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.763e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1719.1\n",
      "No. Observations:                9000   AIC:                            -3432.\n",
      "Df Residuals:                    8997   BIC:                            -3411.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0770      0.064     95.255      0.000       5.952       6.202\n",
      "x1             0.9864      0.011     92.774      0.000       0.966       1.007\n",
      "x2             1.0142      0.011     95.094      0.000       0.993       1.035\n",
      "==============================================================================\n",
      "Omnibus:                        0.749   Durbin-Watson:                   1.969\n",
      "Prob(Omnibus):                  0.688   Jarque-Bera (JB):                0.711\n",
      "Skew:                          -0.016   Prob(JB):                        0.701\n",
      "Kurtosis:                       3.030   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.728e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1675.1\n",
      "No. Observations:                9000   AIC:                            -3344.\n",
      "Df Residuals:                    8997   BIC:                            -3323.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0521      0.064     94.324      0.000       5.926       6.178\n",
      "x1             0.9907      0.011     92.651      0.000       0.970       1.012\n",
      "x2             1.0096      0.011     94.107      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        1.079   Durbin-Watson:                   2.028\n",
      "Prob(Omnibus):                  0.583   Jarque-Bera (JB):                1.046\n",
      "Skew:                          -0.009   Prob(JB):                        0.593\n",
      "Kurtosis:                       3.049   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.710e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1656.5\n",
      "No. Observations:                9000   AIC:                            -3307.\n",
      "Df Residuals:                    8997   BIC:                            -3286.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.1223      0.064     95.153      0.000       5.996       6.248\n",
      "x1             0.9791      0.011     91.282      0.000       0.958       1.000\n",
      "x2             1.0212      0.011     94.866      0.000       1.000       1.042\n",
      "==============================================================================\n",
      "Omnibus:                        0.751   Durbin-Watson:                   2.017\n",
      "Prob(Omnibus):                  0.687   Jarque-Bera (JB):                0.714\n",
      "Skew:                           0.002   Prob(JB):                        0.700\n",
      "Kurtosis:                       3.043   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.745e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1698.4\n",
      "No. Observations:                9000   AIC:                            -3391.\n",
      "Df Residuals:                    8997   BIC:                            -3370.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0869      0.064     94.967      0.000       5.961       6.213\n",
      "x1             0.9850      0.011     92.213      0.000       0.964       1.006\n",
      "x2             1.0157      0.011     94.770      0.000       0.995       1.037\n",
      "==============================================================================\n",
      "Omnibus:                        0.236   Durbin-Watson:                   2.010\n",
      "Prob(Omnibus):                  0.889   Jarque-Bera (JB):                0.220\n",
      "Skew:                           0.011   Prob(JB):                        0.896\n",
      "Kurtosis:                       3.010   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.745e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1683.9\n",
      "No. Observations:                9000   AIC:                            -3362.\n",
      "Df Residuals:                    8997   BIC:                            -3340.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0606      0.064     94.202      0.000       5.935       6.187\n",
      "x1             0.9892      0.011     92.264      0.000       0.968       1.010\n",
      "x2             1.0113      0.011     94.010      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        0.897   Durbin-Watson:                   2.009\n",
      "Prob(Omnibus):                  0.639   Jarque-Bera (JB):                0.880\n",
      "Skew:                           0.024   Prob(JB):                        0.644\n",
      "Kurtosis:                       3.010   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.748e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1715.2\n",
      "No. Observations:                9000   AIC:                            -3424.\n",
      "Df Residuals:                    8997   BIC:                            -3403.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0574      0.064     94.539      0.000       5.932       6.183\n",
      "x1             0.9899      0.011     92.722      0.000       0.969       1.011\n",
      "x2             1.0106      0.011     94.372      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        0.521   Durbin-Watson:                   1.996\n",
      "Prob(Omnibus):                  0.771   Jarque-Bera (JB):                0.492\n",
      "Skew:                          -0.015   Prob(JB):                        0.782\n",
      "Kurtosis:                       3.020   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.704e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1670.9\n",
      "No. Observations:                9000   AIC:                            -3336.\n",
      "Df Residuals:                    8997   BIC:                            -3314.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0585      0.065     93.817      0.000       5.932       6.185\n",
      "x1             0.9896      0.011     91.966      0.000       0.968       1.011\n",
      "x2             1.0109      0.011     93.708      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        0.870   Durbin-Watson:                   1.964\n",
      "Prob(Omnibus):                  0.647   Jarque-Bera (JB):                0.835\n",
      "Skew:                           0.005   Prob(JB):                        0.659\n",
      "Kurtosis:                       3.046   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.723e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1680.2\n",
      "No. Observations:                9000   AIC:                            -3354.\n",
      "Df Residuals:                    8997   BIC:                            -3333.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0984      0.064     94.751      0.000       5.972       6.225\n",
      "x1             0.9831      0.011     91.677      0.000       0.962       1.004\n",
      "x2             1.0173      0.011     94.564      0.000       0.996       1.038\n",
      "==============================================================================\n",
      "Omnibus:                        1.510   Durbin-Watson:                   1.970\n",
      "Prob(Omnibus):                  0.470   Jarque-Bera (JB):                1.487\n",
      "Skew:                           0.014   Prob(JB):                        0.475\n",
      "Kurtosis:                       3.056   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.737e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1665.4\n",
      "No. Observations:                9000   AIC:                            -3325.\n",
      "Df Residuals:                    8997   BIC:                            -3303.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0461      0.065     93.714      0.000       5.920       6.173\n",
      "x1             0.9918      0.011     92.253      0.000       0.971       1.013\n",
      "x2             1.0084      0.011     93.498      0.000       0.987       1.030\n",
      "==============================================================================\n",
      "Omnibus:                        2.163   Durbin-Watson:                   1.981\n",
      "Prob(Omnibus):                  0.339   Jarque-Bera (JB):                2.203\n",
      "Skew:                           0.004   Prob(JB):                        0.332\n",
      "Kurtosis:                       3.076   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.732e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1671.0\n",
      "No. Observations:                9000   AIC:                            -3336.\n",
      "Df Residuals:                    8997   BIC:                            -3315.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0644      0.065     93.917      0.000       5.938       6.191\n",
      "x1             0.9889      0.011     91.885      0.000       0.968       1.010\n",
      "x2             1.0114      0.011     93.666      0.000       0.990       1.033\n",
      "==============================================================================\n",
      "Omnibus:                        0.306   Durbin-Watson:                   1.967\n",
      "Prob(Omnibus):                  0.858   Jarque-Bera (JB):                0.274\n",
      "Skew:                           0.008   Prob(JB):                        0.872\n",
      "Kurtosis:                       3.022   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.723e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1661.4\n",
      "No. Observations:                9000   AIC:                            -3317.\n",
      "Df Residuals:                    8997   BIC:                            -3296.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0570      0.064     93.913      0.000       5.931       6.183\n",
      "x1             0.9899      0.011     92.090      0.000       0.969       1.011\n",
      "x2             1.0102      0.011     93.660      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        0.749   Durbin-Watson:                   1.998\n",
      "Prob(Omnibus):                  0.688   Jarque-Bera (JB):                0.711\n",
      "Skew:                          -0.007   Prob(JB):                        0.701\n",
      "Kurtosis:                       3.041   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.719e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1648.1\n",
      "No. Observations:                9000   AIC:                            -3290.\n",
      "Df Residuals:                    8997   BIC:                            -3269.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0757      0.065     94.006      0.000       5.949       6.202\n",
      "x1             0.9868      0.011     91.609      0.000       0.966       1.008\n",
      "x2             1.0140      0.011     93.858      0.000       0.993       1.035\n",
      "==============================================================================\n",
      "Omnibus:                        1.340   Durbin-Watson:                   1.991\n",
      "Prob(Omnibus):                  0.512   Jarque-Bera (JB):                1.321\n",
      "Skew:                          -0.006   Prob(JB):                        0.517\n",
      "Kurtosis:                       3.058   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.744e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1697.2\n",
      "No. Observations:                9000   AIC:                            -3388.\n",
      "Df Residuals:                    8997   BIC:                            -3367.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0464      0.064     94.375      0.000       5.921       6.172\n",
      "x1             0.9916      0.011     92.888      0.000       0.971       1.012\n",
      "x2             1.0090      0.011     94.200      0.000       0.988       1.030\n",
      "==============================================================================\n",
      "Omnibus:                        1.276   Durbin-Watson:                   2.008\n",
      "Prob(Omnibus):                  0.528   Jarque-Bera (JB):                1.256\n",
      "Skew:                          -0.004   Prob(JB):                        0.534\n",
      "Kurtosis:                       3.057   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.751e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1696.2\n",
      "No. Observations:                9000   AIC:                            -3386.\n",
      "Df Residuals:                    8997   BIC:                            -3365.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0822      0.064     94.881      0.000       5.957       6.208\n",
      "x1             0.9856      0.011     92.254      0.000       0.965       1.007\n",
      "x2             1.0149      0.011     94.700      0.000       0.994       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        1.151   Durbin-Watson:                   1.999\n",
      "Prob(Omnibus):                  0.562   Jarque-Bera (JB):                1.125\n",
      "Skew:                           0.004   Prob(JB):                        0.570\n",
      "Kurtosis:                       3.054   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.745e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1686.0\n",
      "No. Observations:                9000   AIC:                            -3366.\n",
      "Df Residuals:                    8997   BIC:                            -3345.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0994      0.065     94.456      0.000       5.973       6.226\n",
      "x1             0.9829      0.011     91.334      0.000       0.962       1.004\n",
      "x2             1.0175      0.011     94.214      0.000       0.996       1.039\n",
      "==============================================================================\n",
      "Omnibus:                        1.372   Durbin-Watson:                   1.986\n",
      "Prob(Omnibus):                  0.504   Jarque-Bera (JB):                1.353\n",
      "Skew:                          -0.007   Prob(JB):                        0.508\n",
      "Kurtosis:                       3.059   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.725e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1668.7\n",
      "No. Observations:                9000   AIC:                            -3331.\n",
      "Df Residuals:                    8997   BIC:                            -3310.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0597      0.064     93.982      0.000       5.933       6.186\n",
      "x1             0.9895      0.011     92.094      0.000       0.968       1.011\n",
      "x2             1.0104      0.011     93.731      0.000       0.989       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        0.713   Durbin-Watson:                   2.014\n",
      "Prob(Omnibus):                  0.700   Jarque-Bera (JB):                0.675\n",
      "Skew:                           0.003   Prob(JB):                        0.714\n",
      "Kurtosis:                       3.042   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.736e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1675.6\n",
      "No. Observations:                9000   AIC:                            -3345.\n",
      "Df Residuals:                    8997   BIC:                            -3324.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0799      0.065     93.985      0.000       5.953       6.207\n",
      "x1             0.9860      0.011     91.468      0.000       0.965       1.007\n",
      "x2             1.0141      0.011     93.779      0.000       0.993       1.035\n",
      "==============================================================================\n",
      "Omnibus:                        0.861   Durbin-Watson:                   2.015\n",
      "Prob(Omnibus):                  0.650   Jarque-Bera (JB):                0.823\n",
      "Skew:                           0.008   Prob(JB):                        0.662\n",
      "Kurtosis:                       3.044   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.733e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1697.0\n",
      "No. Observations:                9000   AIC:                            -3388.\n",
      "Df Residuals:                    8997   BIC:                            -3367.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0901      0.064     94.869      0.000       5.964       6.216\n",
      "x1             0.9843      0.011     92.024      0.000       0.963       1.005\n",
      "x2             1.0164      0.011     94.728      0.000       0.995       1.037\n",
      "==============================================================================\n",
      "Omnibus:                        1.235   Durbin-Watson:                   1.993\n",
      "Prob(Omnibus):                  0.539   Jarque-Bera (JB):                1.213\n",
      "Skew:                           0.003   Prob(JB):                        0.545\n",
      "Kurtosis:                       3.057   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.748e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1687.6\n",
      "No. Observations:                9000   AIC:                            -3369.\n",
      "Df Residuals:                    8997   BIC:                            -3348.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0598      0.064     93.977      0.000       5.933       6.186\n",
      "x1             0.9892      0.011     92.051      0.000       0.968       1.010\n",
      "x2             1.0112      0.011     93.821      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        0.361   Durbin-Watson:                   1.988\n",
      "Prob(Omnibus):                  0.835   Jarque-Bera (JB):                0.324\n",
      "Skew:                           0.002   Prob(JB):                        0.850\n",
      "Kurtosis:                       3.029   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.697e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1658.4\n",
      "No. Observations:                9000   AIC:                            -3311.\n",
      "Df Residuals:                    8997   BIC:                            -3290.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0945      0.065     94.170      0.000       5.968       6.221\n",
      "x1             0.9835      0.011     91.204      0.000       0.962       1.005\n",
      "x2             1.0169      0.011     94.027      0.000       0.996       1.038\n",
      "==============================================================================\n",
      "Omnibus:                        0.883   Durbin-Watson:                   1.995\n",
      "Prob(Omnibus):                  0.643   Jarque-Bera (JB):                0.848\n",
      "Skew:                           0.004   Prob(JB):                        0.654\n",
      "Kurtosis:                       3.047   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.738e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1678.7\n",
      "No. Observations:                9000   AIC:                            -3351.\n",
      "Df Residuals:                    8997   BIC:                            -3330.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0928      0.064     94.603      0.000       5.967       6.219\n",
      "x1             0.9839      0.011     91.677      0.000       0.963       1.005\n",
      "x2             1.0162      0.011     94.352      0.000       0.995       1.037\n",
      "==============================================================================\n",
      "Omnibus:                        0.743   Durbin-Watson:                   1.998\n",
      "Prob(Omnibus):                  0.690   Jarque-Bera (JB):                0.704\n",
      "Skew:                           0.008   Prob(JB):                        0.703\n",
      "Kurtosis:                       3.040   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.766e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1716.6\n",
      "No. Observations:                9000   AIC:                            -3427.\n",
      "Df Residuals:                    8997   BIC:                            -3406.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0477      0.064     94.111      0.000       5.922       6.174\n",
      "x1             0.9914      0.011     92.567      0.000       0.970       1.012\n",
      "x2             1.0093      0.011     93.931      0.000       0.988       1.030\n",
      "==============================================================================\n",
      "Omnibus:                        2.556   Durbin-Watson:                   1.969\n",
      "Prob(Omnibus):                  0.279   Jarque-Bera (JB):                2.634\n",
      "Skew:                          -0.001   Prob(JB):                        0.268\n",
      "Kurtosis:                       3.084   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.729e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1674.3\n",
      "No. Observations:                9000   AIC:                            -3343.\n",
      "Df Residuals:                    8997   BIC:                            -3321.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0372      0.064     93.701      0.000       5.911       6.163\n",
      "x1             0.9932      0.011     92.491      0.000       0.972       1.014\n",
      "x2             1.0070      0.011     93.475      0.000       0.986       1.028\n",
      "==============================================================================\n",
      "Omnibus:                        0.854   Durbin-Watson:                   2.014\n",
      "Prob(Omnibus):                  0.652   Jarque-Bera (JB):                0.819\n",
      "Skew:                          -0.003   Prob(JB):                        0.664\n",
      "Kurtosis:                       3.046   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.722e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1662.7\n",
      "No. Observations:                9000   AIC:                            -3319.\n",
      "Df Residuals:                    8997   BIC:                            -3298.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0876      0.064     94.613      0.000       5.961       6.214\n",
      "x1             0.9847      0.011     91.857      0.000       0.964       1.006\n",
      "x2             1.0157      0.011     94.450      0.000       0.995       1.037\n",
      "==============================================================================\n",
      "Omnibus:                        0.372   Durbin-Watson:                   1.962\n",
      "Prob(Omnibus):                  0.830   Jarque-Bera (JB):                0.337\n",
      "Skew:                           0.005   Prob(JB):                        0.845\n",
      "Kurtosis:                       3.028   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.703e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1647.8\n",
      "No. Observations:                9000   AIC:                            -3290.\n",
      "Df Residuals:                    8997   BIC:                            -3268.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0567      0.064     94.196      0.000       5.931       6.183\n",
      "x1             0.9900      0.011     92.400      0.000       0.969       1.011\n",
      "x2             1.0105      0.011     94.024      0.000       0.989       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        1.114   Durbin-Watson:                   2.026\n",
      "Prob(Omnibus):                  0.573   Jarque-Bera (JB):                1.078\n",
      "Skew:                          -0.013   Prob(JB):                        0.583\n",
      "Kurtosis:                       3.047   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.733e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1706.9\n",
      "No. Observations:                9000   AIC:                            -3408.\n",
      "Df Residuals:                    8997   BIC:                            -3386.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0398      0.064     94.141      0.000       5.914       6.166\n",
      "x1             0.9927      0.011     92.859      0.000       0.972       1.014\n",
      "x2             1.0078      0.011     93.994      0.000       0.987       1.029\n",
      "==============================================================================\n",
      "Omnibus:                        1.227   Durbin-Watson:                   2.017\n",
      "Prob(Omnibus):                  0.541   Jarque-Bera (JB):                1.198\n",
      "Skew:                          -0.010   Prob(JB):                        0.549\n",
      "Kurtosis:                       3.053   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.723e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:42   Log-Likelihood:                 1665.4\n",
      "No. Observations:                9000   AIC:                            -3325.\n",
      "Df Residuals:                    8997   BIC:                            -3304.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0655      0.064     94.389      0.000       5.940       6.191\n",
      "x1             0.9887      0.011     92.324      0.000       0.968       1.010\n",
      "x2             1.0117      0.011     94.168      0.000       0.991       1.033\n",
      "==============================================================================\n",
      "Omnibus:                        0.953   Durbin-Watson:                   1.996\n",
      "Prob(Omnibus):                  0.621   Jarque-Bera (JB):                0.920\n",
      "Skew:                           0.003   Prob(JB):                        0.631\n",
      "Kurtosis:                       3.049   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.725e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1676.1\n",
      "No. Observations:                9000   AIC:                            -3346.\n",
      "Df Residuals:                    8997   BIC:                            -3325.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0889      0.064     94.783      0.000       5.963       6.215\n",
      "x1             0.9845      0.011     91.956      0.000       0.964       1.006\n",
      "x2             1.0155      0.011     94.511      0.000       0.994       1.037\n",
      "==============================================================================\n",
      "Omnibus:                        0.501   Durbin-Watson:                   1.988\n",
      "Prob(Omnibus):                  0.779   Jarque-Bera (JB):                0.462\n",
      "Skew:                          -0.001   Prob(JB):                        0.794\n",
      "Kurtosis:                       3.035   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.703e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1659.7\n",
      "No. Observations:                9000   AIC:                            -3313.\n",
      "Df Residuals:                    8997   BIC:                            -3292.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0789      0.064     94.345      0.000       5.953       6.205\n",
      "x1             0.9864      0.011     91.864      0.000       0.965       1.007\n",
      "x2             1.0142      0.011     94.140      0.000       0.993       1.035\n",
      "==============================================================================\n",
      "Omnibus:                        1.012   Durbin-Watson:                   1.984\n",
      "Prob(Omnibus):                  0.603   Jarque-Bera (JB):                0.981\n",
      "Skew:                          -0.004   Prob(JB):                        0.612\n",
      "Kurtosis:                       3.051   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.687e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1628.6\n",
      "No. Observations:                9000   AIC:                            -3251.\n",
      "Df Residuals:                    8997   BIC:                            -3230.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0356      0.065     93.190      0.000       5.909       6.163\n",
      "x1             0.9935      0.011     92.063      0.000       0.972       1.015\n",
      "x2             1.0067      0.011     92.984      0.000       0.985       1.028\n",
      "==============================================================================\n",
      "Omnibus:                        1.279   Durbin-Watson:                   1.996\n",
      "Prob(Omnibus):                  0.528   Jarque-Bera (JB):                1.259\n",
      "Skew:                          -0.001   Prob(JB):                        0.533\n",
      "Kurtosis:                       3.058   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.730e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1676.0\n",
      "No. Observations:                9000   AIC:                            -3346.\n",
      "Df Residuals:                    8997   BIC:                            -3325.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0863      0.064     94.589      0.000       5.960       6.212\n",
      "x1             0.9850      0.011     91.863      0.000       0.964       1.006\n",
      "x2             1.0153      0.011     94.403      0.000       0.994       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        0.600   Durbin-Watson:                   2.000\n",
      "Prob(Omnibus):                  0.741   Jarque-Bera (JB):                0.561\n",
      "Skew:                          -0.001   Prob(JB):                        0.755\n",
      "Kurtosis:                       3.039   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.744e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1699.8\n",
      "No. Observations:                9000   AIC:                            -3394.\n",
      "Df Residuals:                    8997   BIC:                            -3372.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0493      0.064     94.107      0.000       5.923       6.175\n",
      "x1             0.9912      0.011     92.553      0.000       0.970       1.012\n",
      "x2             1.0093      0.011     93.933      0.000       0.988       1.030\n",
      "==============================================================================\n",
      "Omnibus:                        2.082   Durbin-Watson:                   1.993\n",
      "Prob(Omnibus):                  0.353   Jarque-Bera (JB):                2.112\n",
      "Skew:                          -0.006   Prob(JB):                        0.348\n",
      "Kurtosis:                       3.074   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.754e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1707.9\n",
      "No. Observations:                9000   AIC:                            -3410.\n",
      "Df Residuals:                    8997   BIC:                            -3388.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0773      0.064     94.668      0.000       5.951       6.203\n",
      "x1             0.9863      0.011     92.189      0.000       0.965       1.007\n",
      "x2             1.0145      0.011     94.476      0.000       0.993       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        1.139   Durbin-Watson:                   1.961\n",
      "Prob(Omnibus):                  0.566   Jarque-Bera (JB):                1.112\n",
      "Skew:                          -0.005   Prob(JB):                        0.574\n",
      "Kurtosis:                       3.054   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.744e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1698.8\n",
      "No. Observations:                9000   AIC:                            -3392.\n",
      "Df Residuals:                    8997   BIC:                            -3370.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0582      0.064     94.119      0.000       5.932       6.184\n",
      "x1             0.9898      0.011     92.277      0.000       0.969       1.011\n",
      "x2             1.0106      0.011     93.954      0.000       0.989       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        1.631   Durbin-Watson:                   2.008\n",
      "Prob(Omnibus):                  0.442   Jarque-Bera (JB):                1.625\n",
      "Skew:                          -0.009   Prob(JB):                        0.444\n",
      "Kurtosis:                       3.063   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.753e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1710.3\n",
      "No. Observations:                9000   AIC:                            -3415.\n",
      "Df Residuals:                    8997   BIC:                            -3393.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.1166      0.064     95.358      0.000       5.991       6.242\n",
      "x1             0.9801      0.011     91.700      0.000       0.959       1.001\n",
      "x2             1.0202      0.011     95.124      0.000       0.999       1.041\n",
      "==============================================================================\n",
      "Omnibus:                        0.140   Durbin-Watson:                   2.013\n",
      "Prob(Omnibus):                  0.932   Jarque-Bera (JB):                0.137\n",
      "Skew:                           0.010   Prob(JB):                        0.934\n",
      "Kurtosis:                       3.001   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.757e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1708.0\n",
      "No. Observations:                9000   AIC:                            -3410.\n",
      "Df Residuals:                    8997   BIC:                            -3389.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0818      0.064     95.035      0.000       5.956       6.207\n",
      "x1             0.9858      0.011     92.447      0.000       0.965       1.007\n",
      "x2             1.0147      0.011     94.868      0.000       0.994       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        1.819   Durbin-Watson:                   1.981\n",
      "Prob(Omnibus):                  0.403   Jarque-Bera (JB):                1.829\n",
      "Skew:                           0.006   Prob(JB):                        0.401\n",
      "Kurtosis:                       3.069   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.761e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1714.3\n",
      "No. Observations:                9000   AIC:                            -3423.\n",
      "Df Residuals:                    8997   BIC:                            -3401.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0535      0.064     94.465      0.000       5.928       6.179\n",
      "x1             0.9905      0.011     92.768      0.000       0.970       1.011\n",
      "x2             1.0097      0.011     94.253      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        0.628   Durbin-Watson:                   2.001\n",
      "Prob(Omnibus):                  0.731   Jarque-Bera (JB):                0.589\n",
      "Skew:                           0.001   Prob(JB):                        0.745\n",
      "Kurtosis:                       3.040   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.730e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1679.6\n",
      "No. Observations:                9000   AIC:                            -3353.\n",
      "Df Residuals:                    8997   BIC:                            -3332.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0689      0.064     94.658      0.000       5.943       6.195\n",
      "x1             0.9880      0.011     92.464      0.000       0.967       1.009\n",
      "x2             1.0124      0.011     94.473      0.000       0.991       1.033\n",
      "==============================================================================\n",
      "Omnibus:                        0.556   Durbin-Watson:                   2.013\n",
      "Prob(Omnibus):                  0.757   Jarque-Bera (JB):                0.547\n",
      "Skew:                           0.019   Prob(JB):                        0.761\n",
      "Kurtosis:                       3.005   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.736e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1690.7\n",
      "No. Observations:                9000   AIC:                            -3375.\n",
      "Df Residuals:                    8997   BIC:                            -3354.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0858      0.064     94.712      0.000       5.960       6.212\n",
      "x1             0.9852      0.011     92.019      0.000       0.964       1.006\n",
      "x2             1.0148      0.011     94.493      0.000       0.994       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        1.773   Durbin-Watson:                   2.000\n",
      "Prob(Omnibus):                  0.412   Jarque-Bera (JB):                1.778\n",
      "Skew:                           0.007   Prob(JB):                        0.411\n",
      "Kurtosis:                       3.067   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.714e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1673.3\n",
      "No. Observations:                9000   AIC:                            -3341.\n",
      "Df Residuals:                    8997   BIC:                            -3319.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0581      0.064     94.366      0.000       5.932       6.184\n",
      "x1             0.9898      0.011     92.525      0.000       0.969       1.011\n",
      "x2             1.0106      0.011     94.158      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        1.534   Durbin-Watson:                   1.965\n",
      "Prob(Omnibus):                  0.464   Jarque-Bera (JB):                1.529\n",
      "Skew:                          -0.000   Prob(JB):                        0.466\n",
      "Kurtosis:                       3.064   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.729e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1677.3\n",
      "No. Observations:                9000   AIC:                            -3349.\n",
      "Df Residuals:                    8997   BIC:                            -3327.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.1115      0.064     94.830      0.000       5.985       6.238\n",
      "x1             0.9808      0.011     91.318      0.000       0.960       1.002\n",
      "x2             1.0193      0.011     94.590      0.000       0.998       1.040\n",
      "==============================================================================\n",
      "Omnibus:                        1.011   Durbin-Watson:                   2.033\n",
      "Prob(Omnibus):                  0.603   Jarque-Bera (JB):                0.980\n",
      "Skew:                          -0.002   Prob(JB):                        0.613\n",
      "Kurtosis:                       3.051   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.718e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1678.6\n",
      "No. Observations:                9000   AIC:                            -3351.\n",
      "Df Residuals:                    8997   BIC:                            -3330.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.1166      0.065     94.811      0.000       5.990       6.243\n",
      "x1             0.9799      0.011     91.148      0.000       0.959       1.001\n",
      "x2             1.0202      0.011     94.585      0.000       0.999       1.041\n",
      "==============================================================================\n",
      "Omnibus:                        0.369   Durbin-Watson:                   2.013\n",
      "Prob(Omnibus):                  0.831   Jarque-Bera (JB):                0.333\n",
      "Skew:                           0.001   Prob(JB):                        0.847\n",
      "Kurtosis:                       3.030   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.728e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1684.8\n",
      "No. Observations:                9000   AIC:                            -3364.\n",
      "Df Residuals:                    8997   BIC:                            -3342.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0744      0.064     94.531      0.000       5.948       6.200\n",
      "x1             0.9870      0.011     92.166      0.000       0.966       1.008\n",
      "x2             1.0131      0.011     94.286      0.000       0.992       1.034\n",
      "==============================================================================\n",
      "Omnibus:                        0.505   Durbin-Watson:                   2.035\n",
      "Prob(Omnibus):                  0.777   Jarque-Bera (JB):                0.466\n",
      "Skew:                           0.001   Prob(JB):                        0.792\n",
      "Kurtosis:                       3.035   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.715e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1667.6\n",
      "No. Observations:                9000   AIC:                            -3329.\n",
      "Df Residuals:                    8997   BIC:                            -3308.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0750      0.064     94.370      0.000       5.949       6.201\n",
      "x1             0.9870      0.011     92.010      0.000       0.966       1.008\n",
      "x2             1.0132      0.011     94.147      0.000       0.992       1.034\n",
      "==============================================================================\n",
      "Omnibus:                        2.591   Durbin-Watson:                   1.998\n",
      "Prob(Omnibus):                  0.274   Jarque-Bera (JB):                2.670\n",
      "Skew:                          -0.004   Prob(JB):                        0.263\n",
      "Kurtosis:                       3.084   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.750e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1700.8\n",
      "No. Observations:                9000   AIC:                            -3396.\n",
      "Df Residuals:                    8997   BIC:                            -3374.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0578      0.064     94.551      0.000       5.932       6.183\n",
      "x1             0.9898      0.011     92.705      0.000       0.969       1.011\n",
      "x2             1.0104      0.011     94.336      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        0.739   Durbin-Watson:                   2.000\n",
      "Prob(Omnibus):                  0.691   Jarque-Bera (JB):                0.701\n",
      "Skew:                          -0.002   Prob(JB):                        0.704\n",
      "Kurtosis:                       3.043   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.730e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1694.3\n",
      "No. Observations:                9000   AIC:                            -3383.\n",
      "Df Residuals:                    8997   BIC:                            -3361.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0862      0.064     94.932      0.000       5.960       6.212\n",
      "x1             0.9851      0.011     92.227      0.000       0.964       1.006\n",
      "x2             1.0155      0.011     94.780      0.000       0.995       1.037\n",
      "==============================================================================\n",
      "Omnibus:                        1.471   Durbin-Watson:                   1.987\n",
      "Prob(Omnibus):                  0.479   Jarque-Bera (JB):                1.465\n",
      "Skew:                           0.031   Prob(JB):                        0.481\n",
      "Kurtosis:                       3.002   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.768e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1718.2\n",
      "No. Observations:                9000   AIC:                            -3430.\n",
      "Df Residuals:                    8997   BIC:                            -3409.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0997      0.064     95.058      0.000       5.974       6.226\n",
      "x1             0.9827      0.011     91.889      0.000       0.962       1.004\n",
      "x2             1.0181      0.011     94.894      0.000       0.997       1.039\n",
      "==============================================================================\n",
      "Omnibus:                        0.556   Durbin-Watson:                   2.003\n",
      "Prob(Omnibus):                  0.757   Jarque-Bera (JB):                0.518\n",
      "Skew:                           0.010   Prob(JB):                        0.772\n",
      "Kurtosis:                       3.031   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.734e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1690.1\n",
      "No. Observations:                9000   AIC:                            -3374.\n",
      "Df Residuals:                    8997   BIC:                            -3353.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0582      0.064     94.293      0.000       5.932       6.184\n",
      "x1             0.9895      0.011     92.406      0.000       0.969       1.010\n",
      "x2             1.0109      0.011     94.088      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        0.421   Durbin-Watson:                   1.981\n",
      "Prob(Omnibus):                  0.810   Jarque-Bera (JB):                0.384\n",
      "Skew:                           0.004   Prob(JB):                        0.825\n",
      "Kurtosis:                       3.031   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.719e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1663.4\n",
      "No. Observations:                9000   AIC:                            -3321.\n",
      "Df Residuals:                    8997   BIC:                            -3300.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.1013      0.065     94.587      0.000       5.975       6.228\n",
      "x1             0.9825      0.011     91.387      0.000       0.961       1.004\n",
      "x2             1.0175      0.011     94.337      0.000       0.996       1.039\n",
      "==============================================================================\n",
      "Omnibus:                        0.321   Durbin-Watson:                   2.002\n",
      "Prob(Omnibus):                  0.852   Jarque-Bera (JB):                0.286\n",
      "Skew:                           0.004   Prob(JB):                        0.867\n",
      "Kurtosis:                       3.026   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.736e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1703.0\n",
      "No. Observations:                9000   AIC:                            -3400.\n",
      "Df Residuals:                    8997   BIC:                            -3379.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0520      0.064     94.134      0.000       5.926       6.178\n",
      "x1             0.9909      0.011     92.482      0.000       0.970       1.012\n",
      "x2             1.0095      0.011     93.879      0.000       0.988       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        0.892   Durbin-Watson:                   2.019\n",
      "Prob(Omnibus):                  0.640   Jarque-Bera (JB):                0.856\n",
      "Skew:                          -0.007   Prob(JB):                        0.652\n",
      "Kurtosis:                       3.046   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.723e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1668.8\n",
      "No. Observations:                9000   AIC:                            -3332.\n",
      "Df Residuals:                    8997   BIC:                            -3310.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0972      0.065     94.509      0.000       5.971       6.224\n",
      "x1             0.9831      0.011     91.421      0.000       0.962       1.004\n",
      "x2             1.0176      0.011     94.331      0.000       0.996       1.039\n",
      "==============================================================================\n",
      "Omnibus:                        1.362   Durbin-Watson:                   2.012\n",
      "Prob(Omnibus):                  0.506   Jarque-Bera (JB):                1.335\n",
      "Skew:                           0.012   Prob(JB):                        0.513\n",
      "Kurtosis:                       3.054   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.711e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1660.5\n",
      "No. Observations:                9000   AIC:                            -3315.\n",
      "Df Residuals:                    8997   BIC:                            -3294.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0397      0.064     93.718      0.000       5.913       6.166\n",
      "x1             0.9926      0.011     92.423      0.000       0.972       1.014\n",
      "x2             1.0075      0.011     93.530      0.000       0.986       1.029\n",
      "==============================================================================\n",
      "Omnibus:                        0.490   Durbin-Watson:                   1.995\n",
      "Prob(Omnibus):                  0.783   Jarque-Bera (JB):                0.453\n",
      "Skew:                           0.008   Prob(JB):                        0.797\n",
      "Kurtosis:                       3.030   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.714e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1694.7\n",
      "No. Observations:                9000   AIC:                            -3383.\n",
      "Df Residuals:                    8997   BIC:                            -3362.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0528      0.064     94.581      0.000       5.927       6.178\n",
      "x1             0.9906      0.011     92.881      0.000       0.970       1.011\n",
      "x2             1.0103      0.011     94.414      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        0.562   Durbin-Watson:                   1.998\n",
      "Prob(Omnibus):                  0.755   Jarque-Bera (JB):                0.527\n",
      "Skew:                           0.013   Prob(JB):                        0.768\n",
      "Kurtosis:                       3.027   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.731e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1694.0\n",
      "No. Observations:                9000   AIC:                            -3382.\n",
      "Df Residuals:                    8997   BIC:                            -3361.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0934      0.064     94.842      0.000       5.967       6.219\n",
      "x1             0.9838      0.011     91.881      0.000       0.963       1.005\n",
      "x2             1.0167      0.011     94.660      0.000       0.996       1.038\n",
      "==============================================================================\n",
      "Omnibus:                        0.917   Durbin-Watson:                   2.027\n",
      "Prob(Omnibus):                  0.632   Jarque-Bera (JB):                0.882\n",
      "Skew:                          -0.007   Prob(JB):                        0.643\n",
      "Kurtosis:                       3.047   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.746e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1681.0\n",
      "No. Observations:                9000   AIC:                            -3356.\n",
      "Df Residuals:                    8997   BIC:                            -3335.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0837      0.064     94.862      0.000       5.958       6.209\n",
      "x1             0.9855      0.011     92.228      0.000       0.965       1.006\n",
      "x2             1.0148      0.011     94.653      0.000       0.994       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        2.188   Durbin-Watson:                   1.978\n",
      "Prob(Omnibus):                  0.335   Jarque-Bera (JB):                2.230\n",
      "Skew:                          -0.004   Prob(JB):                        0.328\n",
      "Kurtosis:                       3.077   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.751e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:43   Log-Likelihood:                 1685.3\n",
      "No. Observations:                9000   AIC:                            -3365.\n",
      "Df Residuals:                    8997   BIC:                            -3343.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0588      0.064     94.389      0.000       5.933       6.185\n",
      "x1             0.9898      0.011     92.534      0.000       0.969       1.011\n",
      "x2             1.0108      0.011     94.225      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        0.274   Durbin-Watson:                   1.981\n",
      "Prob(Omnibus):                  0.872   Jarque-Bera (JB):                0.241\n",
      "Skew:                           0.002   Prob(JB):                        0.887\n",
      "Kurtosis:                       3.025   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.724e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1663.2\n",
      "No. Observations:                9000   AIC:                            -3320.\n",
      "Df Residuals:                    8997   BIC:                            -3299.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0523      0.064     94.275      0.000       5.926       6.178\n",
      "x1             0.9907      0.011     92.621      0.000       0.970       1.012\n",
      "x2             1.0095      0.011     94.035      0.000       0.988       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        0.982   Durbin-Watson:                   2.008\n",
      "Prob(Omnibus):                  0.612   Jarque-Bera (JB):                0.948\n",
      "Skew:                           0.008   Prob(JB):                        0.623\n",
      "Kurtosis:                       3.048   Cond. No.                         211.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.711e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1662.1\n",
      "No. Observations:                9000   AIC:                            -3318.\n",
      "Df Residuals:                    8997   BIC:                            -3297.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0687      0.065     94.011      0.000       5.942       6.195\n",
      "x1             0.9880      0.011     91.845      0.000       0.967       1.009\n",
      "x2             1.0122      0.011     93.765      0.000       0.991       1.033\n",
      "==============================================================================\n",
      "Omnibus:                        0.347   Durbin-Watson:                   1.995\n",
      "Prob(Omnibus):                  0.841   Jarque-Bera (JB):                0.313\n",
      "Skew:                          -0.007   Prob(JB):                        0.855\n",
      "Kurtosis:                       3.025   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.743e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1703.5\n",
      "No. Observations:                9000   AIC:                            -3401.\n",
      "Df Residuals:                    8997   BIC:                            -3380.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0618      0.064     94.226      0.000       5.936       6.188\n",
      "x1             0.9890      0.011     92.258      0.000       0.968       1.010\n",
      "x2             1.0113      0.011     94.021      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        1.257   Durbin-Watson:                   1.949\n",
      "Prob(Omnibus):                  0.534   Jarque-Bera (JB):                1.222\n",
      "Skew:                          -0.015   Prob(JB):                        0.543\n",
      "Kurtosis:                       3.048   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.711e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1670.2\n",
      "No. Observations:                9000   AIC:                            -3334.\n",
      "Df Residuals:                    8997   BIC:                            -3313.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0622      0.065     93.939      0.000       5.936       6.189\n",
      "x1             0.9889      0.011     91.951      0.000       0.968       1.010\n",
      "x2             1.0118      0.011     93.838      0.000       0.991       1.033\n",
      "==============================================================================\n",
      "Omnibus:                        0.548   Durbin-Watson:                   1.985\n",
      "Prob(Omnibus):                  0.760   Jarque-Bera (JB):                0.523\n",
      "Skew:                          -0.017   Prob(JB):                        0.770\n",
      "Kurtosis:                       3.016   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.746e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1701.1\n",
      "No. Observations:                9000   AIC:                            -3396.\n",
      "Df Residuals:                    8997   BIC:                            -3375.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0894      0.065     94.404      0.000       5.963       6.216\n",
      "x1             0.9846      0.011     91.587      0.000       0.964       1.006\n",
      "x2             1.0156      0.011     94.129      0.000       0.994       1.037\n",
      "==============================================================================\n",
      "Omnibus:                        1.699   Durbin-Watson:                   2.019\n",
      "Prob(Omnibus):                  0.428   Jarque-Bera (JB):                1.704\n",
      "Skew:                          -0.003   Prob(JB):                        0.427\n",
      "Kurtosis:                       3.067   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.739e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1683.0\n",
      "No. Observations:                9000   AIC:                            -3360.\n",
      "Df Residuals:                    8997   BIC:                            -3339.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0652      0.064     94.108      0.000       5.939       6.191\n",
      "x1             0.9884      0.011     92.016      0.000       0.967       1.009\n",
      "x2             1.0125      0.011     93.958      0.000       0.991       1.034\n",
      "==============================================================================\n",
      "Omnibus:                        0.599   Durbin-Watson:                   2.033\n",
      "Prob(Omnibus):                  0.741   Jarque-Bera (JB):                0.560\n",
      "Skew:                          -0.004   Prob(JB):                        0.756\n",
      "Kurtosis:                       3.038   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.771e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1741.4\n",
      "No. Observations:                9000   AIC:                            -3477.\n",
      "Df Residuals:                    8997   BIC:                            -3456.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0857      0.064     95.204      0.000       5.960       6.211\n",
      "x1             0.9850      0.011     92.469      0.000       0.964       1.006\n",
      "x2             1.0150      0.011     94.985      0.000       0.994       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        1.043   Durbin-Watson:                   2.028\n",
      "Prob(Omnibus):                  0.594   Jarque-Bera (JB):                1.011\n",
      "Skew:                           0.006   Prob(JB):                        0.603\n",
      "Kurtosis:                       3.050   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.704e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1664.6\n",
      "No. Observations:                9000   AIC:                            -3323.\n",
      "Df Residuals:                    8997   BIC:                            -3302.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0856      0.065     94.269      0.000       5.959       6.212\n",
      "x1             0.9852      0.011     91.579      0.000       0.964       1.006\n",
      "x2             1.0153      0.011     94.074      0.000       0.994       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        1.197   Durbin-Watson:                   1.994\n",
      "Prob(Omnibus):                  0.550   Jarque-Bera (JB):                1.165\n",
      "Skew:                          -0.012   Prob(JB):                        0.558\n",
      "Kurtosis:                       3.050   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.719e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1666.1\n",
      "No. Observations:                9000   AIC:                            -3326.\n",
      "Df Residuals:                    8997   BIC:                            -3305.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0277      0.065     93.215      0.000       5.901       6.154\n",
      "x1             0.9947      0.011     92.318      0.000       0.974       1.016\n",
      "x2             1.0055      0.011     92.997      0.000       0.984       1.027\n",
      "==============================================================================\n",
      "Omnibus:                        0.603   Durbin-Watson:                   2.002\n",
      "Prob(Omnibus):                  0.740   Jarque-Bera (JB):                0.566\n",
      "Skew:                           0.013   Prob(JB):                        0.754\n",
      "Kurtosis:                       3.029   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.725e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1664.9\n",
      "No. Observations:                9000   AIC:                            -3324.\n",
      "Df Residuals:                    8997   BIC:                            -3302.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0720      0.065     93.797      0.000       5.945       6.199\n",
      "x1             0.9874      0.011     91.519      0.000       0.966       1.009\n",
      "x2             1.0134      0.011     93.589      0.000       0.992       1.035\n",
      "==============================================================================\n",
      "Omnibus:                        0.013   Durbin-Watson:                   1.987\n",
      "Prob(Omnibus):                  0.994   Jarque-Bera (JB):                0.005\n",
      "Skew:                           0.000   Prob(JB):                        0.997\n",
      "Kurtosis:                       3.004   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.696e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1654.0\n",
      "No. Observations:                9000   AIC:                            -3302.\n",
      "Df Residuals:                    8997   BIC:                            -3281.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0617      0.064     94.186      0.000       5.935       6.188\n",
      "x1             0.9891      0.011     92.217      0.000       0.968       1.010\n",
      "x2             1.0115      0.011     94.004      0.000       0.990       1.033\n",
      "==============================================================================\n",
      "Omnibus:                        1.168   Durbin-Watson:                   1.991\n",
      "Prob(Omnibus):                  0.558   Jarque-Bera (JB):                1.139\n",
      "Skew:                           0.009   Prob(JB):                        0.566\n",
      "Kurtosis:                       3.052   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.733e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1679.1\n",
      "No. Observations:                9000   AIC:                            -3352.\n",
      "Df Residuals:                    8997   BIC:                            -3331.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0576      0.064     94.093      0.000       5.931       6.184\n",
      "x1             0.9897      0.011     92.257      0.000       0.969       1.011\n",
      "x2             1.0109      0.011     93.924      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        1.526   Durbin-Watson:                   2.046\n",
      "Prob(Omnibus):                  0.466   Jarque-Bera (JB):                1.513\n",
      "Skew:                          -0.008   Prob(JB):                        0.469\n",
      "Kurtosis:                       3.061   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.712e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1662.9\n",
      "No. Observations:                9000   AIC:                            -3320.\n",
      "Df Residuals:                    8997   BIC:                            -3298.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0531      0.064     94.009      0.000       5.927       6.179\n",
      "x1             0.9905      0.011     92.311      0.000       0.969       1.012\n",
      "x2             1.0099      0.011     93.825      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        1.493   Durbin-Watson:                   1.971\n",
      "Prob(Omnibus):                  0.474   Jarque-Bera (JB):                1.482\n",
      "Skew:                          -0.006   Prob(JB):                        0.477\n",
      "Kurtosis:                       3.062   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.740e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1675.9\n",
      "No. Observations:                9000   AIC:                            -3346.\n",
      "Df Residuals:                    8997   BIC:                            -3324.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0894      0.064     94.714      0.000       5.963       6.215\n",
      "x1             0.9846      0.011     91.890      0.000       0.964       1.006\n",
      "x2             1.0162      0.011     94.560      0.000       0.995       1.037\n",
      "==============================================================================\n",
      "Omnibus:                        0.702   Durbin-Watson:                   1.951\n",
      "Prob(Omnibus):                  0.704   Jarque-Bera (JB):                0.674\n",
      "Skew:                          -0.019   Prob(JB):                        0.714\n",
      "Kurtosis:                       3.019   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.760e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1704.1\n",
      "No. Observations:                9000   AIC:                            -3402.\n",
      "Df Residuals:                    8997   BIC:                            -3381.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.1228      0.064     95.387      0.000       5.997       6.249\n",
      "x1             0.9789      0.011     91.519      0.000       0.958       1.000\n",
      "x2             1.0212      0.011     95.168      0.000       1.000       1.042\n",
      "==============================================================================\n",
      "Omnibus:                        0.297   Durbin-Watson:                   1.996\n",
      "Prob(Omnibus):                  0.862   Jarque-Bera (JB):                0.267\n",
      "Skew:                          -0.008   Prob(JB):                        0.875\n",
      "Kurtosis:                       3.021   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.731e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1688.4\n",
      "No. Observations:                9000   AIC:                            -3371.\n",
      "Df Residuals:                    8997   BIC:                            -3350.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0633      0.064     94.855      0.000       5.938       6.189\n",
      "x1             0.9888      0.011     92.816      0.000       0.968       1.010\n",
      "x2             1.0116      0.011     94.660      0.000       0.991       1.033\n",
      "==============================================================================\n",
      "Omnibus:                        1.061   Durbin-Watson:                   2.034\n",
      "Prob(Omnibus):                  0.588   Jarque-Bera (JB):                1.032\n",
      "Skew:                           0.005   Prob(JB):                        0.597\n",
      "Kurtosis:                       3.052   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.724e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1668.1\n",
      "No. Observations:                9000   AIC:                            -3330.\n",
      "Df Residuals:                    8997   BIC:                            -3309.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0454      0.064     93.879      0.000       5.919       6.172\n",
      "x1             0.9917      0.011     92.426      0.000       0.971       1.013\n",
      "x2             1.0084      0.011     93.674      0.000       0.987       1.030\n",
      "==============================================================================\n",
      "Omnibus:                        1.160   Durbin-Watson:                   1.990\n",
      "Prob(Omnibus):                  0.560   Jarque-Bera (JB):                1.134\n",
      "Skew:                           0.005   Prob(JB):                        0.567\n",
      "Kurtosis:                       3.054   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.715e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1661.4\n",
      "No. Observations:                9000   AIC:                            -3317.\n",
      "Df Residuals:                    8997   BIC:                            -3295.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0622      0.065     93.592      0.000       5.935       6.189\n",
      "x1             0.9892      0.011     91.634      0.000       0.968       1.010\n",
      "x2             1.0114      0.011     93.394      0.000       0.990       1.033\n",
      "==============================================================================\n",
      "Omnibus:                        0.513   Durbin-Watson:                   1.971\n",
      "Prob(Omnibus):                  0.774   Jarque-Bera (JB):                0.475\n",
      "Skew:                           0.006   Prob(JB):                        0.789\n",
      "Kurtosis:                       3.034   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.728e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1674.0\n",
      "No. Observations:                9000   AIC:                            -3342.\n",
      "Df Residuals:                    8997   BIC:                            -3321.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0808      0.064     94.700      0.000       5.955       6.207\n",
      "x1             0.9860      0.011     92.132      0.000       0.965       1.007\n",
      "x2             1.0146      0.011     94.539      0.000       0.994       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        0.597   Durbin-Watson:                   1.957\n",
      "Prob(Omnibus):                  0.742   Jarque-Bera (JB):                0.558\n",
      "Skew:                          -0.005   Prob(JB):                        0.757\n",
      "Kurtosis:                       3.037   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.727e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1680.0\n",
      "No. Observations:                9000   AIC:                            -3354.\n",
      "Df Residuals:                    8997   BIC:                            -3333.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.1111      0.064     95.092      0.000       5.985       6.237\n",
      "x1             0.9808      0.011     91.565      0.000       0.960       1.002\n",
      "x2             1.0199      0.011     94.899      0.000       0.999       1.041\n",
      "==============================================================================\n",
      "Omnibus:                        1.248   Durbin-Watson:                   1.971\n",
      "Prob(Omnibus):                  0.536   Jarque-Bera (JB):                1.227\n",
      "Skew:                           0.000   Prob(JB):                        0.541\n",
      "Kurtosis:                       3.057   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.705e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1674.8\n",
      "No. Observations:                9000   AIC:                            -3344.\n",
      "Df Residuals:                    8997   BIC:                            -3322.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0539      0.065     93.838      0.000       5.927       6.180\n",
      "x1             0.9905      0.011     92.113      0.000       0.969       1.012\n",
      "x2             1.0098      0.011     93.600      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        1.075   Durbin-Watson:                   2.021\n",
      "Prob(Omnibus):                  0.584   Jarque-Bera (JB):                1.042\n",
      "Skew:                           0.010   Prob(JB):                        0.594\n",
      "Kurtosis:                       3.049   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.730e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1664.2\n",
      "No. Observations:                9000   AIC:                            -3322.\n",
      "Df Residuals:                    8997   BIC:                            -3301.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0289      0.064     93.546      0.000       5.903       6.155\n",
      "x1             0.9945      0.011     92.618      0.000       0.973       1.016\n",
      "x2             1.0059      0.011     93.369      0.000       0.985       1.027\n",
      "==============================================================================\n",
      "Omnibus:                        0.565   Durbin-Watson:                   2.006\n",
      "Prob(Omnibus):                  0.754   Jarque-Bera (JB):                0.531\n",
      "Skew:                           0.013   Prob(JB):                        0.767\n",
      "Kurtosis:                       3.027   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.707e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1670.9\n",
      "No. Observations:                9000   AIC:                            -3336.\n",
      "Df Residuals:                    8997   BIC:                            -3314.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0879      0.064     94.482      0.000       5.962       6.214\n",
      "x1             0.9847      0.011     91.694      0.000       0.964       1.006\n",
      "x2             1.0155      0.011     94.231      0.000       0.994       1.037\n",
      "==============================================================================\n",
      "Omnibus:                        0.656   Durbin-Watson:                   1.976\n",
      "Prob(Omnibus):                  0.720   Jarque-Bera (JB):                0.617\n",
      "Skew:                          -0.001   Prob(JB):                        0.734\n",
      "Kurtosis:                       3.041   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.726e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1675.4\n",
      "No. Observations:                9000   AIC:                            -3345.\n",
      "Df Residuals:                    8997   BIC:                            -3323.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0609      0.065     93.769      0.000       5.934       6.188\n",
      "x1             0.9894      0.011     91.855      0.000       0.968       1.011\n",
      "x2             1.0110      0.011     93.562      0.000       0.990       1.032\n",
      "==============================================================================\n",
      "Omnibus:                        0.913   Durbin-Watson:                   1.984\n",
      "Prob(Omnibus):                  0.634   Jarque-Bera (JB):                0.879\n",
      "Skew:                           0.002   Prob(JB):                        0.644\n",
      "Kurtosis:                       3.048   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.732e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1684.1\n",
      "No. Observations:                9000   AIC:                            -3362.\n",
      "Df Residuals:                    8997   BIC:                            -3341.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0758      0.064     94.503      0.000       5.950       6.202\n",
      "x1             0.9868      0.011     92.087      0.000       0.966       1.008\n",
      "x2             1.0138      0.011     94.268      0.000       0.993       1.035\n",
      "==============================================================================\n",
      "Omnibus:                        0.253   Durbin-Watson:                   1.953\n",
      "Prob(Omnibus):                  0.881   Jarque-Bera (JB):                0.225\n",
      "Skew:                          -0.008   Prob(JB):                        0.894\n",
      "Kurtosis:                       3.019   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.737e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1701.6\n",
      "No. Observations:                9000   AIC:                            -3397.\n",
      "Df Residuals:                    8997   BIC:                            -3376.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0130      0.064     93.789      0.000       5.887       6.139\n",
      "x1             0.9971      0.011     93.331      0.000       0.976       1.018\n",
      "x2             1.0031      0.011     93.604      0.000       0.982       1.024\n",
      "==============================================================================\n",
      "Omnibus:                        0.054   Durbin-Watson:                   2.019\n",
      "Prob(Omnibus):                  0.974   Jarque-Bera (JB):                0.043\n",
      "Skew:                           0.004   Prob(JB):                        0.979\n",
      "Kurtosis:                       3.006   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.730e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1685.2\n",
      "No. Observations:                9000   AIC:                            -3364.\n",
      "Df Residuals:                    8997   BIC:                            -3343.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0405      0.064     93.927      0.000       5.914       6.167\n",
      "x1             0.9925      0.011     92.595      0.000       0.972       1.014\n",
      "x2             1.0080      0.011     93.728      0.000       0.987       1.029\n",
      "==============================================================================\n",
      "Omnibus:                        1.246   Durbin-Watson:                   1.998\n",
      "Prob(Omnibus):                  0.536   Jarque-Bera (JB):                1.224\n",
      "Skew:                          -0.002   Prob(JB):                        0.542\n",
      "Kurtosis:                       3.057   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.767e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1713.8\n",
      "No. Observations:                9000   AIC:                            -3422.\n",
      "Df Residuals:                    8997   BIC:                            -3400.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0723      0.064     94.914      0.000       5.947       6.198\n",
      "x1             0.9873      0.011     92.613      0.000       0.966       1.008\n",
      "x2             1.0134      0.011     94.748      0.000       0.992       1.034\n",
      "==============================================================================\n",
      "Omnibus:                        0.868   Durbin-Watson:                   2.008\n",
      "Prob(Omnibus):                  0.648   Jarque-Bera (JB):                0.833\n",
      "Skew:                           0.001   Prob(JB):                        0.659\n",
      "Kurtosis:                       3.047   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.689e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:44   Log-Likelihood:                 1643.0\n",
      "No. Observations:                9000   AIC:                            -3280.\n",
      "Df Residuals:                    8997   BIC:                            -3259.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0774      0.065     93.937      0.000       5.951       6.204\n",
      "x1             0.9865      0.011     91.504      0.000       0.965       1.008\n",
      "x2             1.0138      0.011     93.727      0.000       0.993       1.035\n",
      "==============================================================================\n",
      "Omnibus:                        0.327   Durbin-Watson:                   1.965\n",
      "Prob(Omnibus):                  0.849   Jarque-Bera (JB):                0.292\n",
      "Skew:                          -0.001   Prob(JB):                        0.864\n",
      "Kurtosis:                       3.028   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.765e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:45   Log-Likelihood:                 1705.1\n",
      "No. Observations:                9000   AIC:                            -3404.\n",
      "Df Residuals:                    8997   BIC:                            -3383.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0828      0.064     94.401      0.000       5.957       6.209\n",
      "x1             0.9858      0.011     91.795      0.000       0.965       1.007\n",
      "x2             1.0150      0.011     94.195      0.000       0.994       1.036\n",
      "==============================================================================\n",
      "Omnibus:                        0.174   Durbin-Watson:                   1.972\n",
      "Prob(Omnibus):                  0.917   Jarque-Bera (JB):                0.146\n",
      "Skew:                           0.003   Prob(JB):                        0.929\n",
      "Kurtosis:                       3.019   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.771e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:45   Log-Likelihood:                 1724.3\n",
      "No. Observations:                9000   AIC:                            -3443.\n",
      "Df Residuals:                    8997   BIC:                            -3421.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0778      0.064     95.091      0.000       5.953       6.203\n",
      "x1             0.9864      0.011     92.620      0.000       0.966       1.007\n",
      "x2             1.0142      0.011     94.906      0.000       0.993       1.035\n",
      "==============================================================================\n",
      "Omnibus:                        0.829   Durbin-Watson:                   2.002\n",
      "Prob(Omnibus):                  0.661   Jarque-Bera (JB):                0.845\n",
      "Skew:                           0.023   Prob(JB):                        0.655\n",
      "Kurtosis:                       2.987   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.746e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:45   Log-Likelihood:                 1685.3\n",
      "No. Observations:                9000   AIC:                            -3365.\n",
      "Df Residuals:                    8997   BIC:                            -3343.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.1046      0.064     95.332      0.000       5.979       6.230\n",
      "x1             0.9819      0.011     92.014      0.000       0.961       1.003\n",
      "x2             1.0185      0.011     95.115      0.000       0.997       1.039\n",
      "==============================================================================\n",
      "Omnibus:                        0.091   Durbin-Watson:                   2.037\n",
      "Prob(Omnibus):                  0.955   Jarque-Bera (JB):                0.070\n",
      "Skew:                          -0.000   Prob(JB):                        0.965\n",
      "Kurtosis:                       3.014   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.766e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:45   Log-Likelihood:                 1704.0\n",
      "No. Observations:                9000   AIC:                            -3402.\n",
      "Df Residuals:                    8997   BIC:                            -3381.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0647      0.064     94.322      0.000       5.939       6.191\n",
      "x1             0.9887      0.011     92.263      0.000       0.968       1.010\n",
      "x2             1.0117      0.011     94.118      0.000       0.991       1.033\n",
      "==============================================================================\n",
      "Omnibus:                        0.742   Durbin-Watson:                   2.018\n",
      "Prob(Omnibus):                  0.690   Jarque-Bera (JB):                0.712\n",
      "Skew:                           0.019   Prob(JB):                        0.700\n",
      "Kurtosis:                       3.020   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.786e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:45   Log-Likelihood:                 1731.5\n",
      "No. Observations:                9000   AIC:                            -3457.\n",
      "Df Residuals:                    8997   BIC:                            -3436.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0373      0.064     94.568      0.000       5.912       6.162\n",
      "x1             0.9932      0.011     93.350      0.000       0.972       1.014\n",
      "x2             1.0070      0.011     94.365      0.000       0.986       1.028\n",
      "==============================================================================\n",
      "Omnibus:                        0.342   Durbin-Watson:                   1.983\n",
      "Prob(Omnibus):                  0.843   Jarque-Bera (JB):                0.306\n",
      "Skew:                           0.002   Prob(JB):                        0.858\n",
      "Kurtosis:                       3.028   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.694e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:45   Log-Likelihood:                 1653.5\n",
      "No. Observations:                9000   AIC:                            -3301.\n",
      "Df Residuals:                    8997   BIC:                            -3280.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0749      0.064     94.387      0.000       5.949       6.201\n",
      "x1             0.9869      0.011     92.004      0.000       0.966       1.008\n",
      "x2             1.0132      0.011     94.147      0.000       0.992       1.034\n",
      "==============================================================================\n",
      "Omnibus:                        0.756   Durbin-Watson:                   2.014\n",
      "Prob(Omnibus):                  0.685   Jarque-Bera (JB):                0.718\n",
      "Skew:                           0.007   Prob(JB):                        0.698\n",
      "Kurtosis:                       3.041   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.722e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:45   Log-Likelihood:                 1684.9\n",
      "No. Observations:                9000   AIC:                            -3364.\n",
      "Df Residuals:                    8997   BIC:                            -3342.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0542      0.064     94.323      0.000       5.928       6.180\n",
      "x1             0.9905      0.011     92.592      0.000       0.970       1.011\n",
      "x2             1.0098      0.011     94.073      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        1.507   Durbin-Watson:                   1.982\n",
      "Prob(Omnibus):                  0.471   Jarque-Bera (JB):                1.475\n",
      "Skew:                           0.019   Prob(JB):                        0.478\n",
      "Kurtosis:                       3.050   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.749e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:45   Log-Likelihood:                 1719.9\n",
      "No. Observations:                9000   AIC:                            -3434.\n",
      "Df Residuals:                    8997   BIC:                            -3412.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0511      0.064     94.448      0.000       5.925       6.177\n",
      "x1             0.9908      0.011     92.790      0.000       0.970       1.012\n",
      "x2             1.0099      0.011     94.269      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        0.038   Durbin-Watson:                   2.036\n",
      "Prob(Omnibus):                  0.981   Jarque-Bera (JB):                0.036\n",
      "Skew:                           0.005   Prob(JB):                        0.982\n",
      "Kurtosis:                       3.000   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.724e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:45   Log-Likelihood:                 1673.3\n",
      "No. Observations:                9000   AIC:                            -3341.\n",
      "Df Residuals:                    8997   BIC:                            -3319.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0544      0.065     93.834      0.000       5.928       6.181\n",
      "x1             0.9901      0.011     92.087      0.000       0.969       1.011\n",
      "x2             1.0103      0.011     93.642      0.000       0.989       1.031\n",
      "==============================================================================\n",
      "Omnibus:                        0.896   Durbin-Watson:                   1.996\n",
      "Prob(Omnibus):                  0.639   Jarque-Bera (JB):                0.859\n",
      "Skew:                           0.008   Prob(JB):                        0.651\n",
      "Kurtosis:                       3.045   Cond. No.                         213.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator\n",
      "INFO:dowhy.causal_estimator:b: Outcome~Treatment+w0\n",
      "INFO:dowhy.causal_refuters.data_subset_refuter:Making use of Bootstrap as we have more than 100 examples.\n",
      "                 Note: The greater the number of examples, the more accurate are the confidence estimates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                 3.709e+06\n",
      "Date:                Tue, 02 Jun 2020   Prob (F-statistic):               0.00\n",
      "Time:                        21:37:45   Log-Likelihood:                 1660.4\n",
      "No. Observations:                9000   AIC:                            -3315.\n",
      "Df Residuals:                    8997   BIC:                            -3293.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.0239      0.065     93.274      0.000       5.897       6.151\n",
      "x1             0.9955      0.011     92.496      0.000       0.974       1.017\n",
      "x2             1.0051      0.011     93.072      0.000       0.984       1.026\n",
      "==============================================================================\n",
      "Omnibus:                        0.713   Durbin-Watson:                   2.009\n",
      "Prob(Omnibus):                  0.700   Jarque-Bera (JB):                0.679\n",
      "Skew:                          -0.017   Prob(JB):                        0.712\n",
      "Kurtosis:                       3.025   Cond. No.                         212.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "Refute: Use a subset of data\n",
      "Estimated effect:0.9882504484355463\n",
      "New effect:0.9877533007838712\n",
      "p value:0.5\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 删除数据的随机子集\n",
    "res_subset=model.refute_estimate(identified_estimand, estimate,\n",
    "        method_name=\"data_subset_refuter\", subset_fraction=0.9)\n",
    "print(res_subset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# 从敏感性分析的结果来看，对于简单的反驳，DoWhy的因果估计器鲁棒性很好"
   ]
  }
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